{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0001","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=1(x−(0))²+(0)，a=1≠0。求 q(0)，保留整數精確值。","answer":{"kind":"short_text","value":"0","explanation_zh":"q(0)=0。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062001,"parameters":{"a":1,"h":0,"k":0,"x":0,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"vertex_evaluation\",\"0\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0002","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-2(x−(-11))²+(-9)，a=-2≠0。求 q(-13)，保留整數精確值。","answer":{"kind":"short_text","value":"-17","explanation_zh":"q(-13)=-17。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062002,"parameters":{"a":-2,"h":-11,"k":-9,"x":-13,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-2\",\"4\",\"-9\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0003","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=3(x−(-10))²+(-8)，a=3≠0。求 q(-7)，保留整數精確值。","answer":{"kind":"short_text","value":"19","explanation_zh":"q(-7)=19。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062003,"parameters":{"a":3,"h":-10,"k":-8,"x":-7,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"3\",\"9\",\"-8\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0004","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-4(x−(-9))²+(-7)，a=-4≠0。求 q(-13)，保留整數精確值。","answer":{"kind":"short_text","value":"-71","explanation_zh":"q(-13)=-71。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062004,"parameters":{"a":-4,"h":-9,"k":-7,"x":-13,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-4\",\"16\",\"-7\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0005","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=5(x−(-8))²+(-6)，a=5≠0。求 q(-3)，保留整數精確值。","answer":{"kind":"short_text","value":"119","explanation_zh":"q(-3)=119。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062005,"parameters":{"a":5,"h":-8,"k":-6,"x":-3,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"5\",\"25\",\"-6\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0006","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-6(x−(-7))²+(-5)，a=-6≠0。求 q(-8)，保留整數精確值。","answer":{"kind":"short_text","value":"-11","explanation_zh":"q(-8)=-11。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062006,"parameters":{"a":-6,"h":-7,"k":-5,"x":-8,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-6\",\"1\",\"-5\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0007","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=7(x−(-6))²+(-4)，a=7≠0。求 q(-4)，保留整數精確值。","answer":{"kind":"short_text","value":"24","explanation_zh":"q(-4)=24。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062007,"parameters":{"a":7,"h":-6,"k":-4,"x":-4,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"7\",\"4\",\"-4\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0008","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-8(x−(-5))²+(-3)，a=-8≠0。求 q(-8)，保留整數精確值。","answer":{"kind":"short_text","value":"-75","explanation_zh":"q(-8)=-75。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062008,"parameters":{"a":-8,"h":-5,"k":-3,"x":-8,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-8\",\"9\",\"-3\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0009","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=9(x−(-4))²+(-2)，a=9≠0。求 q(0)，保留整數精確值。","answer":{"kind":"short_text","value":"142","explanation_zh":"q(0)=142。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062009,"parameters":{"a":9,"h":-4,"k":-2,"x":0,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"9\",\"16\",\"-2\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0010","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-10(x−(-3))²+(-1)，a=-10≠0。求 q(-8)，保留整數精確值。","answer":{"kind":"short_text","value":"-251","explanation_zh":"q(-8)=-251。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062010,"parameters":{"a":-10,"h":-3,"k":-1,"x":-8,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-10\",\"25\",\"-1\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0011","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=11(x−(-2))²+(0)，a=11≠0。求 q(-1)，保留整數精確值。","answer":{"kind":"short_text","value":"11","explanation_zh":"q(-1)=11。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062011,"parameters":{"a":11,"h":-2,"k":0,"x":-1,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"11\",\"1\",\"0\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0012","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-12(x−(-1))²+(1)，a=-12≠0。求 q(-3)，保留整數精確值。","answer":{"kind":"short_text","value":"-47","explanation_zh":"q(-3)=-47。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062012,"parameters":{"a":-12,"h":-1,"k":1,"x":-3,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-12\",\"4\",\"1\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0013","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=13(x−(0))²+(2)，a=13≠0。求 q(3)，保留整數精確值。","answer":{"kind":"short_text","value":"119","explanation_zh":"q(3)=119。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062013,"parameters":{"a":13,"h":0,"k":2,"x":3,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"13\",\"9\",\"2\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0014","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-14(x−(1))²+(3)，a=-14≠0。求 q(-3)，保留整數精確值。","answer":{"kind":"short_text","value":"-221","explanation_zh":"q(-3)=-221。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062014,"parameters":{"a":-14,"h":1,"k":3,"x":-3,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-14\",\"16\",\"3\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0015","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=15(x−(2))²+(4)，a=15≠0。求 q(7)，保留整數精確值。","answer":{"kind":"short_text","value":"379","explanation_zh":"q(7)=379。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062015,"parameters":{"a":15,"h":2,"k":4,"x":7,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"15\",\"25\",\"4\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0016","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-16(x−(3))²+(5)，a=-16≠0。求 q(2)，保留整數精確值。","answer":{"kind":"short_text","value":"-11","explanation_zh":"q(2)=-11。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062016,"parameters":{"a":-16,"h":3,"k":5,"x":2,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-16\",\"1\",\"5\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0017","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=17(x−(4))²+(6)，a=17≠0。求 q(6)，保留整數精確值。","answer":{"kind":"short_text","value":"74","explanation_zh":"q(6)=74。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062017,"parameters":{"a":17,"h":4,"k":6,"x":6,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"17\",\"4\",\"6\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0018","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-18(x−(5))²+(7)，a=-18≠0。求 q(2)，保留整數精確值。","answer":{"kind":"short_text","value":"-155","explanation_zh":"q(2)=-155。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062018,"parameters":{"a":-18,"h":5,"k":7,"x":2,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-18\",\"9\",\"7\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0019","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=19(x−(6))²+(8)，a=19≠0。求 q(10)，保留整數精確值。","answer":{"kind":"short_text","value":"312","explanation_zh":"q(10)=312。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062019,"parameters":{"a":19,"h":6,"k":8,"x":10,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"19\",\"16\",\"8\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0020","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-20(x−(7))²+(9)，a=-20≠0。求 q(2)，保留整數精確值。","answer":{"kind":"short_text","value":"-491","explanation_zh":"q(2)=-491。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062020,"parameters":{"a":-20,"h":7,"k":9,"x":2,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-20\",\"25\",\"9\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0021","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=21(x−(8))²+(10)，a=21≠0。求 q(9)，保留整數精確值。","answer":{"kind":"short_text","value":"31","explanation_zh":"q(9)=31。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062021,"parameters":{"a":21,"h":8,"k":10,"x":9,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"21\",\"1\",\"10\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0022","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-22(x−(9))²+(11)，a=-22≠0。求 q(7)，保留整數精確值。","answer":{"kind":"short_text","value":"-77","explanation_zh":"q(7)=-77。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062022,"parameters":{"a":-22,"h":9,"k":11,"x":7,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-22\",\"4\",\"11\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0023","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=23(x−(10))²+(12)，a=23≠0。求 q(13)，保留整數精確值。","answer":{"kind":"short_text","value":"219","explanation_zh":"q(13)=219。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062023,"parameters":{"a":23,"h":10,"k":12,"x":13,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"23\",\"9\",\"12\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0024","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-24(x−(11))²+(13)，a=-24≠0。求 q(7)，保留整數精確值。","answer":{"kind":"short_text","value":"-371","explanation_zh":"q(7)=-371。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062024,"parameters":{"a":-24,"h":11,"k":13,"x":7,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-24\",\"16\",\"13\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0025","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式二次函數的精確值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=25(x−(12))²+(14)，a=25≠0。求 q(17)，保留整數精確值。","answer":{"kind":"short_text","value":"639","explanation_zh":"q(17)=639。先求輸入與 h 的差，再平方、乘非零係數、加 k；平方不保留偏移的正負號。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["頂點式二次函數的精確值"]},"variant":{"family_id":"qf-quadratic-function-evaluation","seed":202610062025,"parameters":{"a":25,"h":12,"k":14,"x":17,"domain":"reals","operation":"quadratic_evaluation","semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"25\",\"25\",\"14\"],\"operation\":\"quadratic_evaluation\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0026","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=1(x−(-12))²+(2)，a=1≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(-12, 2)","explanation_zh":"頂點=(-12, 2)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062026,"parameters":{"a":1,"h":-12,"k":2,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-12\",\"2\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0027","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-2(x−(-11))²+(-1)，a=-2≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(-11, -1)","explanation_zh":"頂點=(-11, -1)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062027,"parameters":{"a":-2,"h":-11,"k":-1,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-11\",\"-1\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0028","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=3(x−(-10))²+(-2)，a=3≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(-10, -2)","explanation_zh":"頂點=(-10, -2)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062028,"parameters":{"a":3,"h":-10,"k":-2,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-10\",\"-2\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0029","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-4(x−(-9))²+(5)，a=-4≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(-9, 5)","explanation_zh":"頂點=(-9, 5)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062029,"parameters":{"a":-4,"h":-9,"k":5,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-9\",\"5\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0030","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=1(x−(-8))²+(-4)，a=1≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(-8, -4)","explanation_zh":"頂點=(-8, -4)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062030,"parameters":{"a":1,"h":-8,"k":-4,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-8\",\"-4\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0031","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-2(x−(-7))²+(-5)，a=-2≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(-7, -5)","explanation_zh":"頂點=(-7, -5)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062031,"parameters":{"a":-2,"h":-7,"k":-5,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-7\",\"-5\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0032","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=3(x−(-6))²+(8)，a=3≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(-6, 8)","explanation_zh":"頂點=(-6, 8)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062032,"parameters":{"a":3,"h":-6,"k":8,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-6\",\"8\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0033","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-4(x−(-5))²+(-7)，a=-4≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(-5, -7)","explanation_zh":"頂點=(-5, -7)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062033,"parameters":{"a":-4,"h":-5,"k":-7,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-5\",\"-7\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0034","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=1(x−(-4))²+(-8)，a=1≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(-4, -8)","explanation_zh":"頂點=(-4, -8)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062034,"parameters":{"a":1,"h":-4,"k":-8,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-4\",\"-8\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0035","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-2(x−(-3))²+(11)，a=-2≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(-3, 11)","explanation_zh":"頂點=(-3, 11)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062035,"parameters":{"a":-2,"h":-3,"k":11,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-3\",\"11\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0036","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=3(x−(-2))²+(-10)，a=3≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(-2, -10)","explanation_zh":"頂點=(-2, -10)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062036,"parameters":{"a":3,"h":-2,"k":-10,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-2\",\"-10\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0037","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-4(x−(-1))²+(-11)，a=-4≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(-1, -11)","explanation_zh":"頂點=(-1, -11)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062037,"parameters":{"a":-4,"h":-1,"k":-11,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-1\",\"-11\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0038","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=1(x−(0))²+(14)，a=1≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(0, 14)","explanation_zh":"頂點=(0, 14)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062038,"parameters":{"a":1,"h":0,"k":14,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"0\",\"14\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0039","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-2(x−(1))²+(-13)，a=-2≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(1, -13)","explanation_zh":"頂點=(1, -13)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062039,"parameters":{"a":-2,"h":1,"k":-13,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"1\",\"-13\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0040","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=3(x−(2))²+(-14)，a=3≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(2, -14)","explanation_zh":"頂點=(2, -14)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062040,"parameters":{"a":3,"h":2,"k":-14,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"2\",\"-14\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0041","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-4(x−(3))²+(17)，a=-4≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(3, 17)","explanation_zh":"頂點=(3, 17)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062041,"parameters":{"a":-4,"h":3,"k":17,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"3\",\"17\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0042","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=1(x−(4))²+(-16)，a=1≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(4, -16)","explanation_zh":"頂點=(4, -16)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062042,"parameters":{"a":1,"h":4,"k":-16,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"4\",\"-16\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0043","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-2(x−(5))²+(-17)，a=-2≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(5, -17)","explanation_zh":"頂點=(5, -17)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062043,"parameters":{"a":-2,"h":5,"k":-17,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"5\",\"-17\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0044","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=3(x−(6))²+(20)，a=3≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(6, 20)","explanation_zh":"頂點=(6, 20)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062044,"parameters":{"a":3,"h":6,"k":20,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"6\",\"20\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0045","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-4(x−(7))²+(-19)，a=-4≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(7, -19)","explanation_zh":"頂點=(7, -19)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062045,"parameters":{"a":-4,"h":7,"k":-19,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"7\",\"-19\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0046","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=1(x−(8))²+(-20)，a=1≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(8, -20)","explanation_zh":"頂點=(8, -20)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062046,"parameters":{"a":1,"h":8,"k":-20,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"8\",\"-20\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0047","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-2(x−(9))²+(23)，a=-2≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(9, 23)","explanation_zh":"頂點=(9, 23)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062047,"parameters":{"a":-2,"h":9,"k":23,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"9\",\"23\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0048","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=3(x−(10))²+(-22)，a=3≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(10, -22)","explanation_zh":"頂點=(10, -22)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062048,"parameters":{"a":3,"h":10,"k":-22,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"10\",\"-22\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0049","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-4(x−(11))²+(-23)，a=-4≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(11, -23)","explanation_zh":"頂點=(11, -23)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062049,"parameters":{"a":-4,"h":11,"k":-23,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"11\",\"-23\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0050","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"頂點式的頂點座標","stem_zh":"在全實數論域，指定 q:R→R，q(x)=1(x−(12))²+(26)，a=1≠0。求拋物線頂點的有序對。","answer":{"kind":"expression","value":"(12, 26)","explanation_zh":"頂點=(12, 26)。平方項在 x=h 為零，因此頂點為 (h,k)；a 的大小不改變頂點座標。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["頂點式的頂點座標"]},"variant":{"family_id":"qf-quadratic-function-vertex","seed":202610062050,"parameters":{"a":1,"h":12,"k":26,"domain":"reals","operation":"quadratic_vertex","semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"12\",\"26\"],\"operation\":\"quadratic_vertex\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0051","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=1(x−(-7))²+(-12)，a=1≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最小值=-12","explanation_zh":"全域最小值=-12。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062051,"parameters":{"a":1,"h":-7,"k":-12,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"-12\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0052","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-2(x−(-6))²+(-11)，a=-2≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最大值=-11","explanation_zh":"全域最大值=-11。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062052,"parameters":{"a":-2,"h":-6,"k":-11,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"-11\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0053","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=3(x−(-5))²+(-10)，a=3≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最小值=-10","explanation_zh":"全域最小值=-10。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062053,"parameters":{"a":3,"h":-5,"k":-10,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"-10\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0054","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-4(x−(-4))²+(-9)，a=-4≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最大值=-9","explanation_zh":"全域最大值=-9。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062054,"parameters":{"a":-4,"h":-4,"k":-9,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"-9\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0055","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=1(x−(-3))²+(-8)，a=1≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最小值=-8","explanation_zh":"全域最小值=-8。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062055,"parameters":{"a":1,"h":-3,"k":-8,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"-8\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0056","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-2(x−(-2))²+(-7)，a=-2≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最大值=-7","explanation_zh":"全域最大值=-7。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062056,"parameters":{"a":-2,"h":-2,"k":-7,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"-7\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0057","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=3(x−(-1))²+(-6)，a=3≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最小值=-6","explanation_zh":"全域最小值=-6。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062057,"parameters":{"a":3,"h":-1,"k":-6,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"-6\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0058","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-4(x−(0))²+(-5)，a=-4≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最大值=-5","explanation_zh":"全域最大值=-5。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062058,"parameters":{"a":-4,"h":0,"k":-5,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"-5\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0059","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=1(x−(1))²+(-4)，a=1≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最小值=-4","explanation_zh":"全域最小值=-4。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062059,"parameters":{"a":1,"h":1,"k":-4,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"-4\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0060","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-2(x−(2))²+(-3)，a=-2≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最大值=-3","explanation_zh":"全域最大值=-3。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062060,"parameters":{"a":-2,"h":2,"k":-3,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"-3\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0061","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=3(x−(3))²+(-2)，a=3≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最小值=-2","explanation_zh":"全域最小值=-2。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062061,"parameters":{"a":3,"h":3,"k":-2,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"-2\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0062","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-4(x−(4))²+(-1)，a=-4≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最大值=-1","explanation_zh":"全域最大值=-1。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062062,"parameters":{"a":-4,"h":4,"k":-1,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"-1\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0063","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=1(x−(5))²+(0)，a=1≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最小值=0","explanation_zh":"全域最小值=0。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062063,"parameters":{"a":1,"h":5,"k":0,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"0\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0064","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-2(x−(6))²+(1)，a=-2≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最大值=1","explanation_zh":"全域最大值=1。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062064,"parameters":{"a":-2,"h":6,"k":1,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"1\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0065","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=3(x−(7))²+(2)，a=3≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最小值=2","explanation_zh":"全域最小值=2。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062065,"parameters":{"a":3,"h":7,"k":2,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"2\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0066","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-4(x−(8))²+(3)，a=-4≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最大值=3","explanation_zh":"全域最大值=3。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062066,"parameters":{"a":-4,"h":8,"k":3,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"3\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0067","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=1(x−(9))²+(4)，a=1≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最小值=4","explanation_zh":"全域最小值=4。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062067,"parameters":{"a":1,"h":9,"k":4,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"4\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0068","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-2(x−(10))²+(5)，a=-2≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最大值=5","explanation_zh":"全域最大值=5。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062068,"parameters":{"a":-2,"h":10,"k":5,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"5\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0069","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=3(x−(11))²+(6)，a=3≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最小值=6","explanation_zh":"全域最小值=6。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062069,"parameters":{"a":3,"h":11,"k":6,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"6\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0070","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-4(x−(12))²+(7)，a=-4≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最大值=7","explanation_zh":"全域最大值=7。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062070,"parameters":{"a":-4,"h":12,"k":7,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"7\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0071","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=1(x−(13))²+(8)，a=1≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最小值=8","explanation_zh":"全域最小值=8。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062071,"parameters":{"a":1,"h":13,"k":8,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"8\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0072","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-2(x−(14))²+(9)，a=-2≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最大值=9","explanation_zh":"全域最大值=9。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062072,"parameters":{"a":-2,"h":14,"k":9,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"9\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0073","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=3(x−(15))²+(10)，a=3≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最小值=10","explanation_zh":"全域最小值=10。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062073,"parameters":{"a":3,"h":15,"k":10,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"10\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0074","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-4(x−(16))²+(11)，a=-4≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最大值=11","explanation_zh":"全域最大值=11。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062074,"parameters":{"a":-4,"h":16,"k":11,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"11\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0075","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"全實數二次函數的全域極值","stem_zh":"在全實數論域，指定 q:R→R，q(x)=1(x−(17))²+(12)，a=1≠0。指出全域最小值或全域最大值，並給出該值；不限制成有限輸入區間。","answer":{"kind":"short_text","value":"全域最小值=12","explanation_zh":"全域最小值=12。平方項非負，a>0 時 q(x)≥k，a<0 時 q(x)≤k，並在 x=h 取得等號。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["全實數二次函數的全域極值"]},"variant":{"family_id":"qf-quadratic-function-extremum","seed":202610062075,"parameters":{"a":1,"h":17,"k":12,"domain":"reals","operation":"quadratic_extremum","semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"12\"],\"operation\":\"quadratic_extremum\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0076","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=1(x−(0))²+(0)，a=1≠0。圖形點 (0,q(0)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(0, 0)","explanation_zh":"對稱點=(0, 0)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062076,"parameters":{"a":1,"h":0,"k":0,"x":0,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"1\",\"0\",\"0\",\"0\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0077","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-2(x−(-11))²+(-9)，a=-2≠0。圖形點 (-13,q(-13)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(-9, -17)","explanation_zh":"對稱點=(-9, -17)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062077,"parameters":{"a":-2,"h":-11,"k":-9,"x":-13,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-2\",\"-11\",\"-9\",\"-13\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0078","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=3(x−(-10))²+(-8)，a=3≠0。圖形點 (-7,q(-7)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(-13, 19)","explanation_zh":"對稱點=(-13, 19)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062078,"parameters":{"a":3,"h":-10,"k":-8,"x":-7,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"3\",\"-10\",\"-8\",\"-7\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0079","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-4(x−(-9))²+(-7)，a=-4≠0。圖形點 (-13,q(-13)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(-5, -71)","explanation_zh":"對稱點=(-5, -71)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062079,"parameters":{"a":-4,"h":-9,"k":-7,"x":-13,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-4\",\"-9\",\"-7\",\"-13\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0080","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=5(x−(-8))²+(-6)，a=5≠0。圖形點 (-3,q(-3)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(-13, 119)","explanation_zh":"對稱點=(-13, 119)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062080,"parameters":{"a":5,"h":-8,"k":-6,"x":-3,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"5\",\"-8\",\"-6\",\"-3\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0081","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-6(x−(-7))²+(-5)，a=-6≠0。圖形點 (-8,q(-8)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(-6, -11)","explanation_zh":"對稱點=(-6, -11)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062081,"parameters":{"a":-6,"h":-7,"k":-5,"x":-8,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-6\",\"-7\",\"-5\",\"-8\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0082","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=7(x−(-6))²+(-4)，a=7≠0。圖形點 (-4,q(-4)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(-8, 24)","explanation_zh":"對稱點=(-8, 24)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062082,"parameters":{"a":7,"h":-6,"k":-4,"x":-4,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"7\",\"-6\",\"-4\",\"-4\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0083","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-8(x−(-5))²+(-3)，a=-8≠0。圖形點 (-8,q(-8)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(-2, -75)","explanation_zh":"對稱點=(-2, -75)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062083,"parameters":{"a":-8,"h":-5,"k":-3,"x":-8,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-8\",\"-5\",\"-3\",\"-8\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0084","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=9(x−(-4))²+(-2)，a=9≠0。圖形點 (0,q(0)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(-8, 142)","explanation_zh":"對稱點=(-8, 142)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062084,"parameters":{"a":9,"h":-4,"k":-2,"x":0,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"9\",\"-4\",\"-2\",\"0\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0085","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-10(x−(-3))²+(-1)，a=-10≠0。圖形點 (-8,q(-8)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(2, -251)","explanation_zh":"對稱點=(2, -251)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062085,"parameters":{"a":-10,"h":-3,"k":-1,"x":-8,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-10\",\"-3\",\"-1\",\"-8\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0086","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=11(x−(-2))²+(0)，a=11≠0。圖形點 (-1,q(-1)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(-3, 11)","explanation_zh":"對稱點=(-3, 11)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062086,"parameters":{"a":11,"h":-2,"k":0,"x":-1,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"11\",\"-2\",\"0\",\"-1\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0087","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-12(x−(-1))²+(1)，a=-12≠0。圖形點 (-3,q(-3)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(1, -47)","explanation_zh":"對稱點=(1, -47)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062087,"parameters":{"a":-12,"h":-1,"k":1,"x":-3,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-12\",\"-1\",\"1\",\"-3\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0088","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=13(x−(0))²+(2)，a=13≠0。圖形點 (3,q(3)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(-3, 119)","explanation_zh":"對稱點=(-3, 119)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062088,"parameters":{"a":13,"h":0,"k":2,"x":3,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"13\",\"0\",\"2\",\"3\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0089","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-14(x−(1))²+(3)，a=-14≠0。圖形點 (-3,q(-3)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(5, -221)","explanation_zh":"對稱點=(5, -221)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062089,"parameters":{"a":-14,"h":1,"k":3,"x":-3,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-14\",\"1\",\"3\",\"-3\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0090","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=15(x−(2))²+(4)，a=15≠0。圖形點 (7,q(7)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(-3, 379)","explanation_zh":"對稱點=(-3, 379)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062090,"parameters":{"a":15,"h":2,"k":4,"x":7,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"15\",\"2\",\"4\",\"7\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0091","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-16(x−(3))²+(5)，a=-16≠0。圖形點 (2,q(2)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(4, -11)","explanation_zh":"對稱點=(4, -11)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062091,"parameters":{"a":-16,"h":3,"k":5,"x":2,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-16\",\"3\",\"5\",\"2\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0092","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=17(x−(4))²+(6)，a=17≠0。圖形點 (6,q(6)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(2, 74)","explanation_zh":"對稱點=(2, 74)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062092,"parameters":{"a":17,"h":4,"k":6,"x":6,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"17\",\"4\",\"6\",\"6\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0093","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-18(x−(5))²+(7)，a=-18≠0。圖形點 (2,q(2)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(8, -155)","explanation_zh":"對稱點=(8, -155)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062093,"parameters":{"a":-18,"h":5,"k":7,"x":2,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-18\",\"5\",\"7\",\"2\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0094","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=19(x−(6))²+(8)，a=19≠0。圖形點 (10,q(10)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(2, 312)","explanation_zh":"對稱點=(2, 312)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062094,"parameters":{"a":19,"h":6,"k":8,"x":10,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"19\",\"6\",\"8\",\"10\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0095","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-20(x−(7))²+(9)，a=-20≠0。圖形點 (2,q(2)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(12, -491)","explanation_zh":"對稱點=(12, -491)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062095,"parameters":{"a":-20,"h":7,"k":9,"x":2,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-20\",\"7\",\"9\",\"2\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0096","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=21(x−(8))²+(10)，a=21≠0。圖形點 (9,q(9)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(7, 31)","explanation_zh":"對稱點=(7, 31)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062096,"parameters":{"a":21,"h":8,"k":10,"x":9,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"21\",\"8\",\"10\",\"9\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0097","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-22(x−(9))²+(11)，a=-22≠0。圖形點 (7,q(7)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(11, -77)","explanation_zh":"對稱點=(11, -77)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062097,"parameters":{"a":-22,"h":9,"k":11,"x":7,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-22\",\"9\",\"11\",\"7\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0098","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=23(x−(10))²+(12)，a=23≠0。圖形點 (13,q(13)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(7, 219)","explanation_zh":"對稱點=(7, 219)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062098,"parameters":{"a":23,"h":10,"k":12,"x":13,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"23\",\"10\",\"12\",\"13\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0099","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=-24(x−(11))²+(13)，a=-24≠0。圖形點 (7,q(7)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(15, -371)","explanation_zh":"對稱點=(15, -371)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062099,"parameters":{"a":-24,"h":11,"k":13,"x":7,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-24\",\"11\",\"13\",\"7\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261005-advance-20261006-r02-quadratic-function-0100","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","language":"zh-Hant","source_mko_ids":["mko-quadratic-function"],"title_zh":"對稱軸另一側的圖形點","stem_zh":"在全實數論域，指定 q:R→R，q(x)=25(x−(12))²+(14)，a=25≠0。圖形點 (17,q(17)) 關於直線 x=h 的對稱點為何？允許點恰在對稱軸上。","answer":{"kind":"expression","value":"(7, 639)","explanation_zh":"對稱點=(7, 639)。反射後輸入為 h+(h−x)，兩側到 h 的差互為相反數而平方相等，輸出不變。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["對稱軸另一側的圖形點"]},"variant":{"family_id":"qf-quadratic-function-axis-mirror","seed":202610062100,"parameters":{"a":25,"h":12,"k":14,"x":17,"domain":"reals","operation":"quadratic_mirror","semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"25\",\"12\",\"14\",\"17\"],\"operation\":\"quadratic_mirror\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-05","contract_version":"ocme-question-factory-v0.1"}}