# Vertex-Form Quadratic Function Foundations

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batch-20261005-advance-20261006-r02-quadratic-function-foundations · 2026-10-05 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.



## 1. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(1)(x−(0))²+(0), with a≠0. Evaluate q(0) exactly.

View answer and explanation0

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0001/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 2. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(-2)(x−(-11))²+(-9), with a≠0. Evaluate q(-13) exactly.

View answer and explanation-17

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0002/)

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## 3. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(3)(x−(-10))²+(-8), with a≠0. Evaluate q(-7) exactly.

View answer and explanation19

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0003/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 4. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(-4)(x−(-9))²+(-7), with a≠0. Evaluate q(-13) exactly.

View answer and explanation-71

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0004/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 5. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(5)(x−(-8))²+(-6), with a≠0. Evaluate q(-3) exactly.

View answer and explanation119

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0005/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 6. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(-6)(x−(-7))²+(-5), with a≠0. Evaluate q(-8) exactly.

View answer and explanation-11

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0006/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 7. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(7)(x−(-6))²+(-4), with a≠0. Evaluate q(-4) exactly.

View answer and explanation24

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0007/)

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## 8. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(-8)(x−(-5))²+(-3), with a≠0. Evaluate q(-8) exactly.

View answer and explanation-75

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0008/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 9. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(9)(x−(-4))²+(-2), with a≠0. Evaluate q(0) exactly.

View answer and explanation142

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0009/)

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## 10. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(-10)(x−(-3))²+(-1), with a≠0. Evaluate q(-8) exactly.

View answer and explanation-251

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0010/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 11. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(11)(x−(-2))²+(0), with a≠0. Evaluate q(-1) exactly.

View answer and explanation11

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0011/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 12. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(-12)(x−(-1))²+(1), with a≠0. Evaluate q(-3) exactly.

View answer and explanation-47

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0012/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 13. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(13)(x−(0))²+(2), with a≠0. Evaluate q(3) exactly.

View answer and explanation119

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0013/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 14. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(-14)(x−(1))²+(3), with a≠0. Evaluate q(-3) exactly.

View answer and explanation-221

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0014/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 15. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(15)(x−(2))²+(4), with a≠0. Evaluate q(7) exactly.

View answer and explanation379

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0015/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 16. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(-16)(x−(3))²+(5), with a≠0. Evaluate q(2) exactly.

View answer and explanation-11

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0016/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 17. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(17)(x−(4))²+(6), with a≠0. Evaluate q(6) exactly.

View answer and explanation74

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0017/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 18. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(-18)(x−(5))²+(7), with a≠0. Evaluate q(2) exactly.

View answer and explanation-155

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0018/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 19. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(19)(x−(6))²+(8), with a≠0. Evaluate q(10) exactly.

View answer and explanation312

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0019/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 20. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(-20)(x−(7))²+(9), with a≠0. Evaluate q(2) exactly.

View answer and explanation-491

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0020/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 21. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(21)(x−(8))²+(10), with a≠0. Evaluate q(9) exactly.

View answer and explanation31

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0021/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 22. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(-22)(x−(9))²+(11), with a≠0. Evaluate q(7) exactly.

View answer and explanation-77

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0022/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 23. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(23)(x−(10))²+(12), with a≠0. Evaluate q(13) exactly.

View answer and explanation219

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0023/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 24. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(-24)(x−(11))²+(13), with a≠0. Evaluate q(7) exactly.

View answer and explanation-371

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0024/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 25. Exact Evaluation of a Vertex-Form Quadratic

On the full real domain, let q:R→R be q(x)=(25)(x−(12))²+(14), with a≠0. Evaluate q(17) exactly.

View answer and explanation639

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0025/)

Quadratic functions in vertex form · qf-quadratic-function-evaluation · candidate





## 26. Vertex Coordinates in Vertex Form

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.

View answer and explanation(-12, 2)

The vertex is (h,k)=(-12, 2), not merely the scalar extremum value k. Its axis is x=-12.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0026/)

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## 27. Vertex Coordinates in Vertex Form

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.

View answer and explanation(-11, -1)

The vertex is (h,k)=(-11, -1), not merely the scalar extremum value k. Its axis is x=-11.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0027/)

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## 28. Vertex Coordinates in Vertex Form

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.

View answer and explanation(-10, -2)

The vertex is (h,k)=(-10, -2), not merely the scalar extremum value k. Its axis is x=-10.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0028/)

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## 29. Vertex Coordinates in Vertex Form

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.

View answer and explanation(-9, 5)

The vertex is (h,k)=(-9, 5), not merely the scalar extremum value k. Its axis is x=-9.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0029/)

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## 30. Vertex Coordinates in Vertex Form

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.

View answer and explanation(-8, -4)

The vertex is (h,k)=(-8, -4), not merely the scalar extremum value k. Its axis is x=-8.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0030/)

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## 31. Vertex Coordinates in Vertex Form

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.

View answer and explanation(-7, -5)

The vertex is (h,k)=(-7, -5), not merely the scalar extremum value k. Its axis is x=-7.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0031/)

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## 32. Vertex Coordinates in Vertex Form

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.

View answer and explanation(-6, 8)

The vertex is (h,k)=(-6, 8), not merely the scalar extremum value k. Its axis is x=-6.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0032/)

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## 33. Vertex Coordinates in Vertex Form

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.

View answer and explanation(-5, -7)

The vertex is (h,k)=(-5, -7), not merely the scalar extremum value k. Its axis is x=-5.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0033/)

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## 34. Vertex Coordinates in Vertex Form

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.

View answer and explanation(-4, -8)

The vertex is (h,k)=(-4, -8), not merely the scalar extremum value k. Its axis is x=-4.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0034/)

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## 35. Vertex Coordinates in Vertex Form

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.

View answer and explanation(-3, 11)

The vertex is (h,k)=(-3, 11), not merely the scalar extremum value k. Its axis is x=-3.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0035/)

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## 36. Vertex Coordinates in Vertex Form

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.

View answer and explanation(-2, -10)

The vertex is (h,k)=(-2, -10), not merely the scalar extremum value k. Its axis is x=-2.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0036/)

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## 37. Vertex Coordinates in Vertex Form

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.

View answer and explanation(-1, -11)

The vertex is (h,k)=(-1, -11), not merely the scalar extremum value k. Its axis is x=-1.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0037/)

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## 38. Vertex Coordinates in Vertex Form

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.

View answer and explanation(0, 14)

The vertex is (h,k)=(0, 14), not merely the scalar extremum value k. Its axis is x=0.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0038/)

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## 39. Vertex Coordinates in Vertex Form

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.

View answer and explanation(1, -13)

The vertex is (h,k)=(1, -13), not merely the scalar extremum value k. Its axis is x=1.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0039/)

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## 40. Vertex Coordinates in Vertex Form

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.

View answer and explanation(2, -14)

The vertex is (h,k)=(2, -14), not merely the scalar extremum value k. Its axis is x=2.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0040/)

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## 41. Vertex Coordinates in Vertex Form

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.

View answer and explanation(3, 17)

The vertex is (h,k)=(3, 17), not merely the scalar extremum value k. Its axis is x=3.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0041/)

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## 42. Vertex Coordinates in Vertex Form

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.

View answer and explanation(4, -16)

The vertex is (h,k)=(4, -16), not merely the scalar extremum value k. Its axis is x=4.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0042/)

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## 43. Vertex Coordinates in Vertex Form

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.

View answer and explanation(5, -17)

The vertex is (h,k)=(5, -17), not merely the scalar extremum value k. Its axis is x=5.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0043/)

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## 44. Vertex Coordinates in Vertex Form

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.

View answer and explanation(6, 20)

The vertex is (h,k)=(6, 20), not merely the scalar extremum value k. Its axis is x=6.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0044/)

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## 45. Vertex Coordinates in Vertex Form

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.

View answer and explanation(7, -19)

The vertex is (h,k)=(7, -19), not merely the scalar extremum value k. Its axis is x=7.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0045/)

Quadratic functions in vertex form · qf-quadratic-function-vertex · candidate





## 46. Vertex Coordinates in Vertex Form

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.

View answer and explanation(8, -20)

The vertex is (h,k)=(8, -20), not merely the scalar extremum value k. Its axis is x=8.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0046/)

Quadratic functions in vertex form · qf-quadratic-function-vertex · candidate





## 47. Vertex Coordinates in Vertex Form

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.

View answer and explanation(9, 23)

The vertex is (h,k)=(9, 23), not merely the scalar extremum value k. Its axis is x=9.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0047/)

Quadratic functions in vertex form · qf-quadratic-function-vertex · candidate





## 48. Vertex Coordinates in Vertex Form

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.

View answer and explanation(10, -22)

The vertex is (h,k)=(10, -22), not merely the scalar extremum value k. Its axis is x=10.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0048/)

Quadratic functions in vertex form · qf-quadratic-function-vertex · candidate





## 49. Vertex Coordinates in Vertex Form

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.

View answer and explanation(11, -23)

The vertex is (h,k)=(11, -23), not merely the scalar extremum value k. Its axis is x=11.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0049/)

Quadratic functions in vertex form · qf-quadratic-function-vertex · candidate





## 50. Vertex Coordinates in Vertex Form

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.

View answer and explanation(12, 26)

The vertex is (h,k)=(12, 26), not merely the scalar extremum value k. Its axis is x=12.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0050/)

Quadratic functions in vertex form · qf-quadratic-function-vertex · candidate





## 51. Global Extremum over All Real Inputs

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.

View answer and explanationglobal minimum=-12

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0051/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 52. Global Extremum over All Real Inputs

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.

View answer and explanationglobal maximum=-11

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0052/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 53. Global Extremum over All Real Inputs

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.

View answer and explanationglobal minimum=-10

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0053/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 54. Global Extremum over All Real Inputs

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.

View answer and explanationglobal maximum=-9

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0054/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 55. Global Extremum over All Real Inputs

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.

View answer and explanationglobal minimum=-8

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0055/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 56. Global Extremum over All Real Inputs

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.

View answer and explanationglobal maximum=-7

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0056/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 57. Global Extremum over All Real Inputs

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.

View answer and explanationglobal minimum=-6

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0057/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 58. Global Extremum over All Real Inputs

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.

View answer and explanationglobal maximum=-5

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0058/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 59. Global Extremum over All Real Inputs

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.

View answer and explanationglobal minimum=-4

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0059/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 60. Global Extremum over All Real Inputs

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.

View answer and explanationglobal maximum=-3

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0060/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 61. Global Extremum over All Real Inputs

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.

View answer and explanationglobal minimum=-2

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0061/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 62. Global Extremum over All Real Inputs

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.

View answer and explanationglobal maximum=-1

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0062/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 63. Global Extremum over All Real Inputs

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.

View answer and explanationglobal minimum=0

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0063/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 64. Global Extremum over All Real Inputs

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.

View answer and explanationglobal maximum=1

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0064/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 65. Global Extremum over All Real Inputs

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.

View answer and explanationglobal minimum=2

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0065/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 66. Global Extremum over All Real Inputs

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.

View answer and explanationglobal maximum=3

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0066/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 67. Global Extremum over All Real Inputs

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.

View answer and explanationglobal minimum=4

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0067/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 68. Global Extremum over All Real Inputs

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.

View answer and explanationglobal maximum=5

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0068/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 69. Global Extremum over All Real Inputs

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.

View answer and explanationglobal minimum=6

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0069/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 70. Global Extremum over All Real Inputs

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.

View answer and explanationglobal maximum=7

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0070/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 71. Global Extremum over All Real Inputs

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.

View answer and explanationglobal minimum=8

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0071/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 72. Global Extremum over All Real Inputs

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.

View answer and explanationglobal maximum=9

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0072/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 73. Global Extremum over All Real Inputs

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.

View answer and explanationglobal minimum=10

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0073/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 74. Global Extremum over All Real Inputs

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.

View answer and explanationglobal maximum=11

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0074/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 75. Global Extremum over All Real Inputs

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.

View answer and explanationglobal minimum=12

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0075/)

Quadratic functions in vertex form · qf-quadratic-function-extremum · candidate





## 76. Graph Point Reflected across the Axis

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.

View answer and explanation(0, 0)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0076/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 77. Graph Point Reflected across the Axis

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.

View answer and explanation(-9, -17)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0077/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 78. Graph Point Reflected across the Axis

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.

View answer and explanation(-13, 19)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0078/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 79. Graph Point Reflected across the Axis

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.

View answer and explanation(-5, -71)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0079/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 80. Graph Point Reflected across the Axis

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.

View answer and explanation(-13, 119)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0080/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 81. Graph Point Reflected across the Axis

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.

View answer and explanation(-6, -11)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0081/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 82. Graph Point Reflected across the Axis

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.

View answer and explanation(-8, 24)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0082/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 83. Graph Point Reflected across the Axis

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.

View answer and explanation(-2, -75)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0083/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 84. Graph Point Reflected across the Axis

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.

View answer and explanation(-8, 142)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0084/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 85. Graph Point Reflected across the Axis

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.

View answer and explanation(2, -251)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0085/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 86. Graph Point Reflected across the Axis

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.

View answer and explanation(-3, 11)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0086/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 87. Graph Point Reflected across the Axis

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.

View answer and explanation(1, -47)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0087/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 88. Graph Point Reflected across the Axis

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.

View answer and explanation(-3, 119)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0088/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 89. Graph Point Reflected across the Axis

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.

View answer and explanation(5, -221)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0089/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 90. Graph Point Reflected across the Axis

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.

View answer and explanation(-3, 379)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0090/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 91. Graph Point Reflected across the Axis

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.

View answer and explanation(4, -11)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0091/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 92. Graph Point Reflected across the Axis

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.

View answer and explanation(2, 74)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0092/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 93. Graph Point Reflected across the Axis

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.

View answer and explanation(8, -155)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0093/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 94. Graph Point Reflected across the Axis

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.

View answer and explanation(2, 312)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0094/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 95. Graph Point Reflected across the Axis

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.

View answer and explanation(12, -491)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0095/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 96. Graph Point Reflected across the Axis

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.

View answer and explanation(7, 31)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0096/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 97. Graph Point Reflected across the Axis

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.

View answer and explanation(11, -77)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0097/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 98. Graph Point Reflected across the Axis

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.

View answer and explanation(7, 219)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0098/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 99. Graph Point Reflected across the Axis

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.

View answer and explanation(15, -371)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0099/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate





## 100. Graph Point Reflected across the Axis

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.

View answer and explanation(7, 639)

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.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261005-advance-20261006-r02-quadratic-function-0100/)

Quadratic functions in vertex form · qf-quadratic-function-axis-mirror · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261005-advance-20261006-r02-quadratic-function-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261005-advance-20261006-r02-quadratic-function-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261005-advance-20261006-r02-quadratic-function-foundations/validation-report.json)