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Convert a quadratic to vertex form

11th grade (Year 12 in England) · 16 questions · Common Core: HSF.IF.C.8.A, HSA.SSE.B.3.B · England: A-level Pure Mathematics

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  1. Question 1

    Write y = 2x² + 8x + 13 in vertex form.

    • A. y = (x + 4)² + 5
    • B. y = 2(x + 2)² + 13
    • C. y = 2(x + 2)² + 5
    • D. y = 2(x − 2)² + 5

  2. Question 2

    Write y = x² + 6x + 1 in vertex form.

    • A. y = (x + 6)² − 8
    • B. y = (x + 3)² − 8
    • C. y = (x + 3)² + 1
    • D. y = (x − 3)² − 8

  3. Question 3

    Write y = −x² − 8x − 22 in vertex form.

    • A. y = −(x − 4)² − 6
    • B. y = (x − 4)² − 6
    • C. y = −(x + 4)² − 22
    • D. y = −(x + 4)² − 6

  4. Question 4

    Write y = x² − 2x + 12 in vertex form.

    • A. y = (x + 1)² + 11
    • B. y = (x − 1)² + 12
    • C. y = (x − 1)² + 11
    • D. y = (x − 2)² + 11

  5. Question 5

    Write y = 2x² − 4x + 9 in vertex form.

    • A. y = 2(x − 1)² + 7
    • B. y = 2(x + 1)² + 7
    • C. y = 2(x − 1)² + 9
    • D. y = (x − 2)² + 7

  6. Question 6

    Write y = x² − 10x + 14 in vertex form.

    • A. y = (x − 5)² + 14
    • B. y = (x + 5)² − 11
    • C. y = (x − 10)² − 11
    • D. y = (x − 5)² − 11

  7. Question 7

    Write y = 3x² + 12x + 20 in vertex form.

    • A. y = (x + 6)² + 8
    • B. y = 3(x + 2)² + 20
    • C. y = 3(x − 2)² + 8
    • D. y = 3(x + 2)² + 8

  8. Question 8

    Write y = x² + 6x + 15 in vertex form.

    • A. y = (x + 3)² + 15
    • B. y = (x + 3)² + 6
    • C. y = (x − 3)² + 6
    • D. y = (x + 6)² + 6

  9. Question 9

    Write y = 3x² − 12x + 2 in vertex form.

    • A. y = (x − 6)² − 10
    • B. y = 3(x − 2)² − 10
    • C. y = 3(x + 2)² − 10
    • D. y = 3(x − 2)² + 2

  10. Question 10

    Write y = x² + 6x + 19 in vertex form.

    • A. y = (x + 6)² + 10
    • B. y = (x − 3)² + 10
    • C. y = (x + 3)² + 10
    • D. y = (x + 3)² + 19

  11. Question 11

    Write y = 3x² − 12x + 10 in vertex form.

    • A. y = 3(x − 2)² + 10
    • B. y = 3(x − 2)² − 2
    • C. y = (x − 6)² − 2
    • D. y = 3(x + 2)² − 2

  12. Question 12

    Write y = x² − 2x + 4 in vertex form.

    • A. y = (x + 1)² + 3
    • B. y = (x − 1)² + 4
    • C. y = (x − 2)² + 3
    • D. y = (x − 1)² + 3

  13. Question 13

    Write y = 3x² + 12x + 6 in vertex form.

    • A. y = (x + 6)² − 6
    • B. y = 3(x + 2)² + 6
    • C. y = 3(x + 2)² − 6
    • D. y = 3(x − 2)² − 6

  14. Question 14

    Write y = x² + 6x + 21 in vertex form.

    • A. y = (x + 3)² + 21
    • B. y = (x + 6)² + 12
    • C. y = (x − 3)² + 12
    • D. y = (x + 3)² + 12

  15. Question 15

    Write y = 3x² − 24x + 51 in vertex form.

    • A. y = 3(x + 4)² + 3
    • B. y = 3(x − 4)² + 3
    • C. y = (x − 12)² + 3
    • D. y = 3(x − 4)² + 51

  16. Question 16

    Write y = x² − 4x in vertex form.

    • A. y = (x − 4)² − 4
    • B. y = (x + 2)² − 4
    • C. y = (x − 2)² − 4
    • D. y = (x − 2)² + 0

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Answer key: Convert a quadratic to vertex form

  1. 1. C. y = 2(x + 2)² + 5

  2. 2. B. y = (x + 3)² − 8

  3. 3. D. y = −(x + 4)² − 6

  4. 4. C. y = (x − 1)² + 11

  5. 5. A. y = 2(x − 1)² + 7

  6. 6. D. y = (x − 5)² − 11

  7. 7. D. y = 3(x + 2)² + 8

  8. 8. B. y = (x + 3)² + 6

  9. 9. B. y = 3(x − 2)² − 10

  10. 10. C. y = (x + 3)² + 10

  11. 11. B. y = 3(x − 2)² − 2

  12. 12. D. y = (x − 1)² + 3

  13. 13. C. y = 3(x + 2)² − 6

  14. 14. D. y = (x + 3)² + 12

  15. 15. B. y = 3(x − 4)² + 3

  16. 16. C. y = (x − 2)² − 4