{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0001","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6dafcc6b6e5c73a44ca2b0ff549302c2f77f1242c5a227ac0c76d7ed7e9a54d6","family_id":"qf-quadratic-function-evaluation","seed":202610062001,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"vertex_evaluation\",\"0\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(1)(x−(0))²+(0), with a≠0. Evaluate q(0) exactly.","answer":{"kind":"short_text","value":"0","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(0)=0. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0002","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4ba2a611caec0a03a3a11d90f4454512d55bcfc7df4a82ebd7089b290c609013","family_id":"qf-quadratic-function-evaluation","seed":202610062002,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-2\",\"4\",\"-9\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(-2)(x−(-11))²+(-9), with a≠0. Evaluate q(-13) exactly.","answer":{"kind":"short_text","value":"-17","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(-13)=-17. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0003","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bc029a90097abc69080a7efa28a425fc4f936599aaacfaa0db74b74e94701d39","family_id":"qf-quadratic-function-evaluation","seed":202610062003,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"3\",\"9\",\"-8\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(3)(x−(-10))²+(-8), with a≠0. Evaluate q(-7) exactly.","answer":{"kind":"short_text","value":"19","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(-7)=19. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0004","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e79f9553450fe0cc778f88bffe76c8dc2c5fc870fc565086f61ab76d1da31b32","family_id":"qf-quadratic-function-evaluation","seed":202610062004,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-4\",\"16\",\"-7\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(-4)(x−(-9))²+(-7), with a≠0. Evaluate q(-13) exactly.","answer":{"kind":"short_text","value":"-71","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(-13)=-71. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0005","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"afe3e156a12ec5fd59bff16ddde63c5508f19a4a589f9413f2512c98a3d93096","family_id":"qf-quadratic-function-evaluation","seed":202610062005,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"5\",\"25\",\"-6\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(5)(x−(-8))²+(-6), with a≠0. Evaluate q(-3) exactly.","answer":{"kind":"short_text","value":"119","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(-3)=119. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0006","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c48c54d233bb1d82bd809bc991d2f0da1705991b9e999f9c0afb35a95c46fa1","family_id":"qf-quadratic-function-evaluation","seed":202610062006,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-6\",\"1\",\"-5\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(-6)(x−(-7))²+(-5), with a≠0. Evaluate q(-8) exactly.","answer":{"kind":"short_text","value":"-11","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(-8)=-11. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0007","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b165294befc389e5ea4de0235cba7d5c7589499c7b123908585217b04c7b2c85","family_id":"qf-quadratic-function-evaluation","seed":202610062007,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"7\",\"4\",\"-4\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(7)(x−(-6))²+(-4), with a≠0. Evaluate q(-4) exactly.","answer":{"kind":"short_text","value":"24","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(-4)=24. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0008","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fe99029ebdbd65b6c291dca33dcdea2923c60d73842492750f9f4f477d4ceddb","family_id":"qf-quadratic-function-evaluation","seed":202610062008,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-8\",\"9\",\"-3\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(-8)(x−(-5))²+(-3), with a≠0. Evaluate q(-8) exactly.","answer":{"kind":"short_text","value":"-75","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(-8)=-75. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0009","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1be447dc7de88c4b277a3a7f4949ab0f9e53b2d552f320e57203e39838e99930","family_id":"qf-quadratic-function-evaluation","seed":202610062009,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"9\",\"16\",\"-2\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(9)(x−(-4))²+(-2), with a≠0. Evaluate q(0) exactly.","answer":{"kind":"short_text","value":"142","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(0)=142. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0010","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f27a1f10f2b41f564638497d295b34871c2f82faa3486b1ae3dac25223bcb3bd","family_id":"qf-quadratic-function-evaluation","seed":202610062010,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-10\",\"25\",\"-1\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(-10)(x−(-3))²+(-1), with a≠0. Evaluate q(-8) exactly.","answer":{"kind":"short_text","value":"-251","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(-8)=-251. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0011","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"57100a423f5fb86954f00857985dc286181aec85a744acf8d67492321563dd56","family_id":"qf-quadratic-function-evaluation","seed":202610062011,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"11\",\"1\",\"0\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(11)(x−(-2))²+(0), with a≠0. Evaluate q(-1) exactly.","answer":{"kind":"short_text","value":"11","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(-1)=11. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0012","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"364c60f111405d0b39f27e9aee2105b1cb8e0a389381d3fa8426ad77d4949ab1","family_id":"qf-quadratic-function-evaluation","seed":202610062012,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-12\",\"4\",\"1\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(-12)(x−(-1))²+(1), with a≠0. Evaluate q(-3) exactly.","answer":{"kind":"short_text","value":"-47","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(-3)=-47. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0013","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"48e6d05d60fb15a40b8350615f9d3fcc8099425dcf9a9fb77cf14f6b3d92e714","family_id":"qf-quadratic-function-evaluation","seed":202610062013,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"13\",\"9\",\"2\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(13)(x−(0))²+(2), with a≠0. Evaluate q(3) exactly.","answer":{"kind":"short_text","value":"119","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(3)=119. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0014","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3187d34704d452875bea1b1bd4b33123dfbc00005b8c0a1f42b10de1a6d51164","family_id":"qf-quadratic-function-evaluation","seed":202610062014,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-14\",\"16\",\"3\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(-14)(x−(1))²+(3), with a≠0. Evaluate q(-3) exactly.","answer":{"kind":"short_text","value":"-221","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(-3)=-221. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0015","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f15fb0d1d1726663842e9410b4099b70113d2ec216307e78df7b60382dd268c2","family_id":"qf-quadratic-function-evaluation","seed":202610062015,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"15\",\"25\",\"4\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(15)(x−(2))²+(4), with a≠0. Evaluate q(7) exactly.","answer":{"kind":"short_text","value":"379","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(7)=379. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0016","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"714570070e49bc788e829d75f7d9694980057a91a2e0fe3adfdc56d97fa5019a","family_id":"qf-quadratic-function-evaluation","seed":202610062016,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-16\",\"1\",\"5\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(-16)(x−(3))²+(5), with a≠0. Evaluate q(2) exactly.","answer":{"kind":"short_text","value":"-11","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(2)=-11. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0017","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"57d65cf0ca8579ce2ecc6dc68ad668157ca45faf199393ef96775e8e960f6c49","family_id":"qf-quadratic-function-evaluation","seed":202610062017,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"17\",\"4\",\"6\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(17)(x−(4))²+(6), with a≠0. Evaluate q(6) exactly.","answer":{"kind":"short_text","value":"74","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(6)=74. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0018","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"04d4b15a8194e6f56bdb46798e870fe9c505c0dd0a02433d1005f36d1268e423","family_id":"qf-quadratic-function-evaluation","seed":202610062018,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-18\",\"9\",\"7\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(-18)(x−(5))²+(7), with a≠0. Evaluate q(2) exactly.","answer":{"kind":"short_text","value":"-155","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(2)=-155. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0019","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c9d89c27de1530ae988b897b3894995b0ca9d8d378e9118cfeac4b3a77fa9182","family_id":"qf-quadratic-function-evaluation","seed":202610062019,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"19\",\"16\",\"8\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(19)(x−(6))²+(8), with a≠0. Evaluate q(10) exactly.","answer":{"kind":"short_text","value":"312","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(10)=312. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0020","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e8a3ecab8c9dcc021e69eebe4d6036387efcff111da5bf5e4715542a4ed0a55d","family_id":"qf-quadratic-function-evaluation","seed":202610062020,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-20\",\"25\",\"9\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(-20)(x−(7))²+(9), with a≠0. Evaluate q(2) exactly.","answer":{"kind":"short_text","value":"-491","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(2)=-491. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0021","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1ed8d51e7f325a00cd66833a6f55d56f926d95623a03626d5c0b43bc18994cce","family_id":"qf-quadratic-function-evaluation","seed":202610062021,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"21\",\"1\",\"10\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(21)(x−(8))²+(10), with a≠0. Evaluate q(9) exactly.","answer":{"kind":"short_text","value":"31","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(9)=31. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0022","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"38e210eb5fcbe7dcf37e2238e7c765cd08cf5dc8c2ea7970d4bae91acc16e14c","family_id":"qf-quadratic-function-evaluation","seed":202610062022,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-22\",\"4\",\"11\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(-22)(x−(9))²+(11), with a≠0. Evaluate q(7) exactly.","answer":{"kind":"short_text","value":"-77","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(7)=-77. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0023","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c19262435fe92e213d4957966bc69726d89646fdcfcd081a56697036daa134d0","family_id":"qf-quadratic-function-evaluation","seed":202610062023,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"23\",\"9\",\"12\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(23)(x−(10))²+(12), with a≠0. Evaluate q(13) exactly.","answer":{"kind":"short_text","value":"219","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(13)=219. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0024","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e95d58883cf860d4c5b4d200e25e9dc8ba30d294adb8aaf268187bc86347408b","family_id":"qf-quadratic-function-evaluation","seed":202610062024,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"-24\",\"16\",\"13\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(-24)(x−(11))²+(13), with a≠0. Evaluate q(7) exactly.","answer":{"kind":"short_text","value":"-371","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(7)=-371. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0025","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3a6c368808b9acdd21219324b6e52aefb7068577ef1acd2e90dcfe7889279b74","family_id":"qf-quadratic-function-evaluation","seed":202610062025,"semantic_template":"qf-quadratic-function-evaluation/{\"inputs\":[\"25\",\"25\",\"14\"],\"operation\":\"quadratic_evaluation\"}"},"fields":{"title":"Exact Evaluation of a Vertex-Form Quadratic","stem":"On the full real domain, let q:R→R be q(x)=(25)(x−(12))²+(14), with a≠0. Evaluate q(17) exactly.","answer":{"kind":"short_text","value":"639","explanation":"Subtract h, square the displacement, multiply by a, and add k: q(17)=639. Retain the coefficient sign; at x=h the square is zero."},"skills":["Exact Evaluation of a Vertex-Form Quadratic"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0026","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2cf10718c22c65f1150b295c39a025ac3806f40dc9c9ff022737c29437cac368","family_id":"qf-quadratic-function-vertex","seed":202610062026,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-12\",\"2\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(1)(x−(-12))²+(2), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(-12, 2)","explanation":"The vertex is (h,k)=(-12, 2), not merely the scalar extremum value k. Its axis is x=-12."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0027","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a65d2e36c7218521ddcbe3d81280bfb8b97fcf1ad011fdd67049d34ee10df375","family_id":"qf-quadratic-function-vertex","seed":202610062027,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-11\",\"-1\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(-2)(x−(-11))²+(-1), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(-11, -1)","explanation":"The vertex is (h,k)=(-11, -1), not merely the scalar extremum value k. Its axis is x=-11."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0028","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f35e20619bcb63747f78dafd5cc9b02e33f87d6cc7209f9a435f7b4e00ff982d","family_id":"qf-quadratic-function-vertex","seed":202610062028,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-10\",\"-2\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(3)(x−(-10))²+(-2), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(-10, -2)","explanation":"The vertex is (h,k)=(-10, -2), not merely the scalar extremum value k. Its axis is x=-10."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0029","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"349ae8107e47811724595b5f325f63ca8510cc8e23cc3308668d9bb5cded5a07","family_id":"qf-quadratic-function-vertex","seed":202610062029,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-9\",\"5\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(-4)(x−(-9))²+(5), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(-9, 5)","explanation":"The vertex is (h,k)=(-9, 5), not merely the scalar extremum value k. Its axis is x=-9."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0030","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1e5fb89429d22e02705d408b97c0abae4c88b68a9d98fe20755d85e823b51aa4","family_id":"qf-quadratic-function-vertex","seed":202610062030,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-8\",\"-4\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(1)(x−(-8))²+(-4), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(-8, -4)","explanation":"The vertex is (h,k)=(-8, -4), not merely the scalar extremum value k. Its axis is x=-8."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0031","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e7745e7a099c93ad4e0d04010d5c5a084f6b365863d4d9a6756a4b32812f4af0","family_id":"qf-quadratic-function-vertex","seed":202610062031,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-7\",\"-5\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(-2)(x−(-7))²+(-5), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(-7, -5)","explanation":"The vertex is (h,k)=(-7, -5), not merely the scalar extremum value k. Its axis is x=-7."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0032","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"58892c59cd33a06fb3817edcd59722ced76c4517aa0f90ac0bf4b61b53be6969","family_id":"qf-quadratic-function-vertex","seed":202610062032,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-6\",\"8\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(3)(x−(-6))²+(8), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(-6, 8)","explanation":"The vertex is (h,k)=(-6, 8), not merely the scalar extremum value k. Its axis is x=-6."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0033","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"717bcf352a35925ca2939b3229dde4cdc4c4c74d2e7b1b751ab5bb30b3223fbb","family_id":"qf-quadratic-function-vertex","seed":202610062033,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-5\",\"-7\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(-4)(x−(-5))²+(-7), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(-5, -7)","explanation":"The vertex is (h,k)=(-5, -7), not merely the scalar extremum value k. Its axis is x=-5."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0034","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"68e50a5f7f896e9a17e56988dcc40769b7f4c8b667796cb80614a79d5d2ed69e","family_id":"qf-quadratic-function-vertex","seed":202610062034,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-4\",\"-8\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(1)(x−(-4))²+(-8), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(-4, -8)","explanation":"The vertex is (h,k)=(-4, -8), not merely the scalar extremum value k. Its axis is x=-4."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0035","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c77c8577f2183d7ffa2da689724bbc1cd1f612718351ac980837622653fc9fc","family_id":"qf-quadratic-function-vertex","seed":202610062035,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-3\",\"11\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(-2)(x−(-3))²+(11), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(-3, 11)","explanation":"The vertex is (h,k)=(-3, 11), not merely the scalar extremum value k. Its axis is x=-3."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0036","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c3a864c540929a5838987ff2017592e289bebd25d499098be0363c508ae50f87","family_id":"qf-quadratic-function-vertex","seed":202610062036,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-2\",\"-10\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(3)(x−(-2))²+(-10), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(-2, -10)","explanation":"The vertex is (h,k)=(-2, -10), not merely the scalar extremum value k. Its axis is x=-2."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0037","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9eb67b4156c3c8a1e4ca5d315771ced6be58f5ff1050610bfe0bb16208c59c63","family_id":"qf-quadratic-function-vertex","seed":202610062037,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"-1\",\"-11\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(-4)(x−(-1))²+(-11), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(-1, -11)","explanation":"The vertex is (h,k)=(-1, -11), not merely the scalar extremum value k. Its axis is x=-1."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0038","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"09a5b9cdaaec60daaa7cf6e9679babc8486e4671eea5b56307957e0347d859ce","family_id":"qf-quadratic-function-vertex","seed":202610062038,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"0\",\"14\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(1)(x−(0))²+(14), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(0, 14)","explanation":"The vertex is (h,k)=(0, 14), not merely the scalar extremum value k. Its axis is x=0."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0039","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e161f19365a7f57c2a684186e122a8e3cdee5cc95d5fa390c6fbcb8359492a18","family_id":"qf-quadratic-function-vertex","seed":202610062039,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"1\",\"-13\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(-2)(x−(1))²+(-13), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(1, -13)","explanation":"The vertex is (h,k)=(1, -13), not merely the scalar extremum value k. Its axis is x=1."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0040","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"897ee3aca7328e51b8e8bee3d6321011192809dfb8cfa7e5f0ccd4829267190f","family_id":"qf-quadratic-function-vertex","seed":202610062040,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"2\",\"-14\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(3)(x−(2))²+(-14), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(2, -14)","explanation":"The vertex is (h,k)=(2, -14), not merely the scalar extremum value k. Its axis is x=2."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0041","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2dd676b5f7b656a52ab460aa8f8d478bffbb99cb0a47e92f734ed0a3e27e2091","family_id":"qf-quadratic-function-vertex","seed":202610062041,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"3\",\"17\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(-4)(x−(3))²+(17), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(3, 17)","explanation":"The vertex is (h,k)=(3, 17), not merely the scalar extremum value k. Its axis is x=3."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0042","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e12f4846698908de5c4d55f88791c79d712bf987b371a41c16a2f86a5bb4ff89","family_id":"qf-quadratic-function-vertex","seed":202610062042,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"4\",\"-16\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(1)(x−(4))²+(-16), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(4, -16)","explanation":"The vertex is (h,k)=(4, -16), not merely the scalar extremum value k. Its axis is x=4."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0043","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"652207561c1e7c952f523e79c289a443270356957ec1545f3932d9a05ee49d39","family_id":"qf-quadratic-function-vertex","seed":202610062043,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"5\",\"-17\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(-2)(x−(5))²+(-17), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(5, -17)","explanation":"The vertex is (h,k)=(5, -17), not merely the scalar extremum value k. Its axis is x=5."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0044","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8bc683fbbc44c423fbe2aa0b8336c5603c268502805b2d9c4b0456869e29f8a1","family_id":"qf-quadratic-function-vertex","seed":202610062044,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"6\",\"20\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(3)(x−(6))²+(20), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(6, 20)","explanation":"The vertex is (h,k)=(6, 20), not merely the scalar extremum value k. Its axis is x=6."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0045","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"20d72e5ae8b1e33908752963762ec6c3afc772f86b9b90b9b32da286ece5512f","family_id":"qf-quadratic-function-vertex","seed":202610062045,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"7\",\"-19\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(-4)(x−(7))²+(-19), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(7, -19)","explanation":"The vertex is (h,k)=(7, -19), not merely the scalar extremum value k. Its axis is x=7."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0046","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"41e1513a3218bad6f9f8573682299d740092b100929cf56db147bd9503bf2008","family_id":"qf-quadratic-function-vertex","seed":202610062046,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"8\",\"-20\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(1)(x−(8))²+(-20), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(8, -20)","explanation":"The vertex is (h,k)=(8, -20), not merely the scalar extremum value k. Its axis is x=8."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0047","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2cdcb8d9d3dcf9e3a1c01dea57eab4c5df50c74ce8572cdc072f4bcf78c094f1","family_id":"qf-quadratic-function-vertex","seed":202610062047,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"9\",\"23\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(-2)(x−(9))²+(23), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(9, 23)","explanation":"The vertex is (h,k)=(9, 23), not merely the scalar extremum value k. Its axis is x=9."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0048","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"da5bc5a7c6fa6956d119e3b958ea822e74c466e932620958d64c55811279f31a","family_id":"qf-quadratic-function-vertex","seed":202610062048,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"10\",\"-22\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(3)(x−(10))²+(-22), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(10, -22)","explanation":"The vertex is (h,k)=(10, -22), not merely the scalar extremum value k. Its axis is x=10."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0049","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2b39d474edfe0debb1c1910cede05381e5dc1ab62bf6e51031a764d9705c3974","family_id":"qf-quadratic-function-vertex","seed":202610062049,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"11\",\"-23\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(-4)(x−(11))²+(-23), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(11, -23)","explanation":"The vertex is (h,k)=(11, -23), not merely the scalar extremum value k. Its axis is x=11."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0050","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5908f49b3fc5b6b2151acf79eeddf1a8db41d8cc9448a33fcb024a7e60ce8db6","family_id":"qf-quadratic-function-vertex","seed":202610062050,"semantic_template":"qf-quadratic-function-vertex/{\"inputs\":[\"12\",\"26\"],\"operation\":\"quadratic_vertex\"}"},"fields":{"title":"Vertex Coordinates in Vertex Form","stem":"On the full real domain, let q:R→R be q(x)=(1)(x−(12))²+(26), with a≠0. Give the vertex as an ordered coordinate pair.","answer":{"kind":"expression","value":"(12, 26)","explanation":"The vertex is (h,k)=(12, 26), not merely the scalar extremum value k. Its axis is x=12."},"skills":["Vertex Coordinates in Vertex Form"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0051","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"50f70088a080a5d7290f05ff4aadfdf466078b683e9cbd69cd443946fee887f6","family_id":"qf-quadratic-function-extremum","seed":202610062051,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"-12\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(1)(x−(-7))²+(-12), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global minimum=-12","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global minimum=-12; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0052","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"37d345460a89c6dd3db98a7778c150bb468e80eeaa783a44e114326a2af2632c","family_id":"qf-quadratic-function-extremum","seed":202610062052,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"-11\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(-2)(x−(-6))²+(-11), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global maximum=-11","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global maximum=-11; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0053","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5c64ca77bbb1deedb366b4e6fa2667821a599d6a8fc8de67e49c985143f86c8d","family_id":"qf-quadratic-function-extremum","seed":202610062053,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"-10\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(3)(x−(-5))²+(-10), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global minimum=-10","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global minimum=-10; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0054","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b1c019058a9f2d5d924d2213521b2b875b74a03da01676091eb5f4ecd9feefa2","family_id":"qf-quadratic-function-extremum","seed":202610062054,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"-9\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(-4)(x−(-4))²+(-9), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global maximum=-9","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global maximum=-9; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0055","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"31b48b397ee081da19434d67bec23eb23e664e411f4b0384243aba2aa5985ec5","family_id":"qf-quadratic-function-extremum","seed":202610062055,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"-8\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(1)(x−(-3))²+(-8), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global minimum=-8","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global minimum=-8; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0056","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"55e43be29cc1c9916358b06510e53b00cef5ffc2619a67069fc9994eeed915f9","family_id":"qf-quadratic-function-extremum","seed":202610062056,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"-7\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(-2)(x−(-2))²+(-7), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global maximum=-7","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global maximum=-7; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0057","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ce3f567cb63616aa50f963f2217482838bc40c5c56ae751c316f2094fbe86eab","family_id":"qf-quadratic-function-extremum","seed":202610062057,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"-6\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(3)(x−(-1))²+(-6), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global minimum=-6","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global minimum=-6; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0058","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8d5e00da01ad2e6619408073d5e45df8e7c91de7192b2b4b936746e82bb39d17","family_id":"qf-quadratic-function-extremum","seed":202610062058,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"-5\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(-4)(x−(0))²+(-5), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global maximum=-5","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global maximum=-5; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0059","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0f9f3856be6c4acab521e7b70b736779f0d8b38eb245bcf5cf97a20f27428506","family_id":"qf-quadratic-function-extremum","seed":202610062059,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"-4\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(1)(x−(1))²+(-4), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global minimum=-4","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global minimum=-4; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0060","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"39a98ca1853ffbf5ae547e6402ab1bf7d38e42822dbba1f9aa0df0760f43af22","family_id":"qf-quadratic-function-extremum","seed":202610062060,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"-3\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(-2)(x−(2))²+(-3), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global maximum=-3","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global maximum=-3; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0061","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"25d34337be44f643f7af16ff48806748967bc125e21932ebc06be15f59be88b8","family_id":"qf-quadratic-function-extremum","seed":202610062061,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"-2\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(3)(x−(3))²+(-2), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global minimum=-2","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global minimum=-2; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0062","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"67505c158a394f08e32c7b1ce69fa69c84a8d195a991357218aea8d7ff996d17","family_id":"qf-quadratic-function-extremum","seed":202610062062,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"-1\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(-4)(x−(4))²+(-1), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global maximum=-1","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global maximum=-1; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0063","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c76e58c5e8919ea707b6ffc90bc42f0d7b57b4422c4b9643e4ce89d81a6aca83","family_id":"qf-quadratic-function-extremum","seed":202610062063,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"0\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(1)(x−(5))²+(0), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global minimum=0","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global minimum=0; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0064","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3daf6c73866411727d6d508f2cd28d13a24ee29586aebab665e69a064e72f33b","family_id":"qf-quadratic-function-extremum","seed":202610062064,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"1\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(-2)(x−(6))²+(1), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global maximum=1","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global maximum=1; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0065","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a5162c96b3dff3b5d31feb9e34ab92183d67533424467a29f6ba80f2c5b105e8","family_id":"qf-quadratic-function-extremum","seed":202610062065,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"2\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(3)(x−(7))²+(2), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global minimum=2","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global minimum=2; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0066","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"12e1205a40127c0ff2caf57a334f3beac8cd878170b1ba815507bde18b65957d","family_id":"qf-quadratic-function-extremum","seed":202610062066,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"3\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(-4)(x−(8))²+(3), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global maximum=3","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global maximum=3; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0067","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"137aa5c089a5d9a79cc6fe6d412313f2835e7d5d37567c26cea9a206fc27d848","family_id":"qf-quadratic-function-extremum","seed":202610062067,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"4\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(1)(x−(9))²+(4), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global minimum=4","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global minimum=4; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0068","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8146f7a5ec534089a7dbbd8f9a1882845f253a1d677e1a61d52ccc7bd4a64371","family_id":"qf-quadratic-function-extremum","seed":202610062068,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"5\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(-2)(x−(10))²+(5), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global maximum=5","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global maximum=5; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0069","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"905fb6a49c291846f11175895fa455b6cf1d4fb683167ebab6ea20985622fe8d","family_id":"qf-quadratic-function-extremum","seed":202610062069,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"6\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(3)(x−(11))²+(6), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global minimum=6","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global minimum=6; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0070","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5d8b82b89918149cd0c075551db979b40ee9d2abb471e6a79d3527a1736abff3","family_id":"qf-quadratic-function-extremum","seed":202610062070,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"7\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(-4)(x−(12))²+(7), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global maximum=7","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global maximum=7; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0071","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"599902308bc6f2329a65441f0f036fb0ed1dcb7e7b72647d241bbc32c51519af","family_id":"qf-quadratic-function-extremum","seed":202610062071,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"8\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(1)(x−(13))²+(8), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global minimum=8","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global minimum=8; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0072","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0b74f1c5b0f0dc67ba0356c4c33f03b7653bf52f04432222e080c7df97e60836","family_id":"qf-quadratic-function-extremum","seed":202610062072,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"9\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(-2)(x−(14))²+(9), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global maximum=9","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global maximum=9; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0073","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"524ba025df6ff1f480b19bb19de23b122665fc7cfffacc3462014c8388fc530c","family_id":"qf-quadratic-function-extremum","seed":202610062073,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"10\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(3)(x−(15))²+(10), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global minimum=10","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global minimum=10; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0074","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7f2a9dce6d7e6fb78bd76a0e1435927be9654238497930dc6f9243e4be639b3e","family_id":"qf-quadratic-function-extremum","seed":202610062074,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"maximum\",\"11\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(-4)(x−(16))²+(11), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global maximum=11","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global maximum=11; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0075","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b63082dfeac7c484ed37f4e799fbe649ee358c40e45252e6bee9da184a50b440","family_id":"qf-quadratic-function-extremum","seed":202610062075,"semantic_template":"qf-quadratic-function-extremum/{\"inputs\":[\"minimum\",\"12\"],\"operation\":\"quadratic_extremum\"}"},"fields":{"title":"Global Extremum over All Real Inputs","stem":"On the full real domain, let q:R→R be q(x)=(1)(x−(17))²+(12), with a≠0. Give the global minimum or global maximum value, according to the coefficient sign. Do not substitute a restricted interval.","answer":{"kind":"short_text","value":"global minimum=12","explanation":"Because (x−h)²≥0, a>0 gives a global minimum and a<0 a global maximum, attained at x=h. Here global minimum=12; the function is unbounded in the other direction."},"skills":["Global Extremum over All Real Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0076","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"99b44b21080151dfeb5b99bb6167d00a0c6d9fff3afc8ee1ee1e20d666122489","family_id":"qf-quadratic-function-axis-mirror","seed":202610062076,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"1\",\"0\",\"0\",\"0\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(1)(x−(0))²+(0), with a≠0. Reflect the graph point (0,q(0)) across x=0. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(0, 0)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (0, 0); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0077","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9f62accae40522016f7781faae9ed3f5e11ad8c6cac30f636cfbe4e81074607d","family_id":"qf-quadratic-function-axis-mirror","seed":202610062077,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-2\",\"-11\",\"-9\",\"-13\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(-2)(x−(-11))²+(-9), with a≠0. Reflect the graph point (-13,q(-13)) across x=-11. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(-9, -17)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (-9, -17); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0078","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"963a5446f974d6a4f1bbc61c46ed1c9d41f8b69b13b8fcd9a70bc860b456b716","family_id":"qf-quadratic-function-axis-mirror","seed":202610062078,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"3\",\"-10\",\"-8\",\"-7\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(3)(x−(-10))²+(-8), with a≠0. Reflect the graph point (-7,q(-7)) across x=-10. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(-13, 19)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (-13, 19); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0079","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"23ebe66a25347298c086838b9b59d5dfd6c71c99666e5ac04067d1cb849a8a68","family_id":"qf-quadratic-function-axis-mirror","seed":202610062079,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-4\",\"-9\",\"-7\",\"-13\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(-4)(x−(-9))²+(-7), with a≠0. Reflect the graph point (-13,q(-13)) across x=-9. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(-5, -71)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (-5, -71); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0080","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8cc03f7810c9ceb9915a90f5df4150e9df2018888d95d455bf65842c60f0c38b","family_id":"qf-quadratic-function-axis-mirror","seed":202610062080,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"5\",\"-8\",\"-6\",\"-3\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(5)(x−(-8))²+(-6), with a≠0. Reflect the graph point (-3,q(-3)) across x=-8. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(-13, 119)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (-13, 119); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0081","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1842ff4eb1df59eb773afd1880a369e3c284d63218b82538aac94d801e4f2621","family_id":"qf-quadratic-function-axis-mirror","seed":202610062081,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-6\",\"-7\",\"-5\",\"-8\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(-6)(x−(-7))²+(-5), with a≠0. Reflect the graph point (-8,q(-8)) across x=-7. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(-6, -11)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (-6, -11); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0082","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ecaeeefbf7b3c939f0d18b873665b631d588e157d6ba2936de98d0f105415f77","family_id":"qf-quadratic-function-axis-mirror","seed":202610062082,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"7\",\"-6\",\"-4\",\"-4\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(7)(x−(-6))²+(-4), with a≠0. Reflect the graph point (-4,q(-4)) across x=-6. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(-8, 24)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (-8, 24); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0083","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"20bed7b5650e01e37b65431d2cf0dc8b10cad36e80a79ee08bf3b440fe33441c","family_id":"qf-quadratic-function-axis-mirror","seed":202610062083,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-8\",\"-5\",\"-3\",\"-8\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(-8)(x−(-5))²+(-3), with a≠0. Reflect the graph point (-8,q(-8)) across x=-5. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(-2, -75)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (-2, -75); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0084","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"958ec9ff98088d7e4e2e16ff5131f97931b90f3db8cb91b93b32d9e513b320b6","family_id":"qf-quadratic-function-axis-mirror","seed":202610062084,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"9\",\"-4\",\"-2\",\"0\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(9)(x−(-4))²+(-2), with a≠0. Reflect the graph point (0,q(0)) across x=-4. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(-8, 142)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (-8, 142); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0085","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c1a8203e174774ab8af99a79cb9cb4372b9311cd406c877844e94a3a316e692","family_id":"qf-quadratic-function-axis-mirror","seed":202610062085,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-10\",\"-3\",\"-1\",\"-8\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(-10)(x−(-3))²+(-1), with a≠0. Reflect the graph point (-8,q(-8)) across x=-3. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(2, -251)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (2, -251); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0086","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"00ec9c3f0c3b4a15fcdf1c2181076a0c1038a69c31d4516654d1e373c50b81c8","family_id":"qf-quadratic-function-axis-mirror","seed":202610062086,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"11\",\"-2\",\"0\",\"-1\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(11)(x−(-2))²+(0), with a≠0. Reflect the graph point (-1,q(-1)) across x=-2. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(-3, 11)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (-3, 11); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0087","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0ae65355b376ef4ecf266cd401199dcfc5587948d027a8fab3107925edf19db8","family_id":"qf-quadratic-function-axis-mirror","seed":202610062087,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-12\",\"-1\",\"1\",\"-3\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(-12)(x−(-1))²+(1), with a≠0. Reflect the graph point (-3,q(-3)) across x=-1. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(1, -47)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (1, -47); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0088","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"573910880852a8d095166d0240822fa37174a26e2f5f761387967ed863b76e5f","family_id":"qf-quadratic-function-axis-mirror","seed":202610062088,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"13\",\"0\",\"2\",\"3\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(13)(x−(0))²+(2), with a≠0. Reflect the graph point (3,q(3)) across x=0. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(-3, 119)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (-3, 119); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0089","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3dc9e4e97d103e88fda7c8865762584d168f0b4a6fde87454f6641c62494fa68","family_id":"qf-quadratic-function-axis-mirror","seed":202610062089,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-14\",\"1\",\"3\",\"-3\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(-14)(x−(1))²+(3), with a≠0. Reflect the graph point (-3,q(-3)) across x=1. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(5, -221)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (5, -221); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0090","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7916e589f8be27f8a14fc43583f5b96617bd0c2adc7ff13b712f6fd8c9e0344e","family_id":"qf-quadratic-function-axis-mirror","seed":202610062090,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"15\",\"2\",\"4\",\"7\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(15)(x−(2))²+(4), with a≠0. Reflect the graph point (7,q(7)) across x=2. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(-3, 379)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (-3, 379); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0091","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b0250130aa8249915bf92d588a62960757290ea79ead7a034c87f666cd8a5809","family_id":"qf-quadratic-function-axis-mirror","seed":202610062091,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-16\",\"3\",\"5\",\"2\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(-16)(x−(3))²+(5), with a≠0. Reflect the graph point (2,q(2)) across x=3. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(4, -11)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (4, -11); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0092","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c9a06874e01958eb5d885fd0b7947d607b43eb7f9cd9273e705add82915d8208","family_id":"qf-quadratic-function-axis-mirror","seed":202610062092,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"17\",\"4\",\"6\",\"6\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(17)(x−(4))²+(6), with a≠0. Reflect the graph point (6,q(6)) across x=4. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(2, 74)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (2, 74); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0093","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"df6f27f7295bf388e95e6b664a70cb00e068a8e1c692acf82800f1579050f4d2","family_id":"qf-quadratic-function-axis-mirror","seed":202610062093,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-18\",\"5\",\"7\",\"2\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(-18)(x−(5))²+(7), with a≠0. Reflect the graph point (2,q(2)) across x=5. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(8, -155)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (8, -155); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0094","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ae23156e0c26d4d4ac6d3c538b19e120cb2a7cc08362478d90efef2fbe60bcea","family_id":"qf-quadratic-function-axis-mirror","seed":202610062094,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"19\",\"6\",\"8\",\"10\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(19)(x−(6))²+(8), with a≠0. Reflect the graph point (10,q(10)) across x=6. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(2, 312)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (2, 312); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0095","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7b29ce31fc54225443a32de32fbe999133bed8191bb5649f7efe37271d7255c6","family_id":"qf-quadratic-function-axis-mirror","seed":202610062095,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-20\",\"7\",\"9\",\"2\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(-20)(x−(7))²+(9), with a≠0. Reflect the graph point (2,q(2)) across x=7. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(12, -491)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (12, -491); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0096","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c95228a64832b9663463b36c4634a237efc272e05d16a023615bf29e2fb69884","family_id":"qf-quadratic-function-axis-mirror","seed":202610062096,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"21\",\"8\",\"10\",\"9\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(21)(x−(8))²+(10), with a≠0. Reflect the graph point (9,q(9)) across x=8. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(7, 31)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (7, 31); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0097","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4bdd57941c4b7abdd2df69cde699893c22b90484c46e490cd6131947b47488a3","family_id":"qf-quadratic-function-axis-mirror","seed":202610062097,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-22\",\"9\",\"11\",\"7\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(-22)(x−(9))²+(11), with a≠0. Reflect the graph point (7,q(7)) across x=9. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(11, -77)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (11, -77); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0098","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9170c9db66fe4642c9e5029bb7a3426232202cf6af804572e298a3333aafbad4","family_id":"qf-quadratic-function-axis-mirror","seed":202610062098,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"23\",\"10\",\"12\",\"13\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(23)(x−(10))²+(12), with a≠0. Reflect the graph point (13,q(13)) across x=10. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(7, 219)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (7, 219); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0099","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"13034d70eceb3c05af6b2cc31119be5e746936035131be37e9da77412760e3c5","family_id":"qf-quadratic-function-axis-mirror","seed":202610062099,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"-24\",\"11\",\"13\",\"7\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(-24)(x−(11))²+(13), with a≠0. Reflect the graph point (7,q(7)) across x=11. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(15, -371)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (15, -371); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r02-quadratic-function-0100","batch_id":"batch-20261005-advance-20261006-r02-quadratic-function-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ead28f0b1ca098f13da3e6986be9618726a4599da9a96e99d6607fbcbd3b4742","family_id":"qf-quadratic-function-axis-mirror","seed":202610062100,"semantic_template":"qf-quadratic-function-axis-mirror/{\"inputs\":[\"25\",\"12\",\"14\",\"17\"],\"operation\":\"quadratic_mirror\"}"},"fields":{"title":"Graph Point Reflected across the Axis","stem":"On the full real domain, let q:R→R be q(x)=(25)(x−(12))²+(14), with a≠0. Reflect the graph point (17,q(17)) across x=12. Give the reflected (input,output) pair.","answer":{"kind":"expression","value":"(7, 639)","explanation":"The reflected input is 2h−x and its squared displacement is unchanged. The reflected point is (7, 639); a point on the axis is its own reflection."},"skills":["Graph Point Reflected across the Axis"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}