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Grade 9 Quadratic Formula & Vertex Worksheet with Answers

Grade 9 (US) · Year 10 (UK) · Class 9 (India) · Math

Unit 8: Going FurtherAdvanced: Algebra II PreviewCCSS A-REI.B.4bAdvanced

Solving quadratics with the quadratic formula and finding the vertex of a parabola. This free high school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

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Quadratic Formula & Vertex

Grade 9 · Math

Score___ / 12

Name

Class

Date

Learning goal: Advanced: Algebra II Preview · CCSS A-REI.B.4b

Directions: Solve each problem. Show your work, then write your answer in the box.

Example

Use the quadratic formula to solve: x² + x - 6 = 0

Answer: x = -3 or x = 2

RememberQuadratics

vertex (lowest point)axis of symmetry (dashed)roots / zeros (green)x = (−b ± √(b² − 4ac)) ÷ 2adiscriminant b² − 4ac: how many roots
  1. 1

    Use the quadratic formula to solve: 3x² - 18x + 15 = 0

    Answer
  2. 2

    Use the quadratic formula to solve: x² - 36 = 0

    Answer
  3. 3

    Find the vertex of y = x² + 8x + 17

    Answer
  4. 4

    Find the vertex of y = 2x² + 8x - 1

    Answer
  5. 5

    Use the quadratic formula to solve: x² - 3x + 2 = 0

    Answer
  6. 6

    Use the quadratic formula to solve: x² + 4x = 0

    Answer
  7. 7

    Use the quadratic formula to solve: 3x² - 9x - 84 = 0

    Answer
  8. 8

    Use the quadratic formula to solve: 2x² - 22x + 60 = 0

    Answer
  9. 9

    Use the quadratic formula to solve: x² + 3x - 4 = 0

    Answer
  10. 10

    Find the vertex of y = x² + 2x + 7

    Answer
  11. 11

    Use the quadratic formula to solve: 2x² - 12x + 16 = 0

    Answer
  12. 12

    Find the vertex of y = x² - 6x + 2

    Answer

★ Challenge corner for fast finishers

If 2^x = 64, what is 4^x?

How did I do?

Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/9/quadratic_formula

Answer key (click to show)
  1. 1.x = 1 or x = 5
  2. 2.x = -6 or x = 6
  3. 3.(-4, 1)
  4. 4.(-2, -9)
  5. 5.x = 1 or x = 2
  6. 6.x = -4 or x = 0
  7. 7.x = -4 or x = 7
  8. 8.x = 5 or x = 6
  9. 9.x = -4 or x = 1
  10. 10.(-1, 6)
  11. 11.x = 2 or x = 4
  12. 12.(3, -7)
  13. ★4096 (challenge corner)

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