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Grade 8 Quadratic Equations Worksheet with Answers

Grade 8 (US) · Year 9 (UK) · Class 8 (India) · Math

Unit 7: Going FurtherAdvanced: Algebra I PreviewCCSS A-REI.B.4bAdvanced

Solving quadratic equations by factoring and finding their roots. This free middle 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 Equations

Grade 8 · Math

Score___ / 12

Name

Class

Date

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

Directions: Use the pictures to help you. Solve each problem. Show your work, then write your answer in the box.

Example

Solve by factoring: 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

    Solve by factoring: x² - 15x + 56 = 0

    x?x?x²?x?x56two numbers that multiply to 56and add to −15
    Answer
  2. 2

    Solve by factoring: x² + 12x + 35 = 0

    x?x?x²?x?x35two numbers that multiply to 35and add to 12
    Answer
  3. 3

    Solve by factoring: x² - x - 30 = 0

    Answer
  4. 4

    Solve by factoring: x² - 5x + 4 = 0

    x?x?x²?x?x4two numbers that multiply to 4and add to −5
    Answer
  5. 5

    Solve by factoring: x² - 4x - 5 = 0

    x?x?x²?x?x−5two numbers that multiply to −5and add to −4
    Answer
  6. 6

    Solve by factoring: x² - 4x - 21 = 0

    x?x?x²?x?x−21two numbers that multiply to −21and add to −4
    Answer
  7. 7

    Solve by factoring: x² - 4x - 32 = 0

    x?x?x²?x?x−32two numbers that multiply to −32and add to −4
    Answer
  8. 8

    Solve by factoring: x² + 11x + 24 = 0

    x?x?x²?x?x24two numbers that multiply to 24and add to 11
    Answer
  9. 9

    Solve by factoring: x² + 9x + 14 = 0

    x?x?x²?x?x14two numbers that multiply to 14and add to 9
    Answer
  10. 10

    Solve by factoring: x² + 4x + 3 = 0

    x?x?x²?x?x3two numbers that multiply to 3and add to 4
    Answer
  11. 11

    Solve by factoring: x² - 3x = 0

    Answer
  12. 12

    Solve by factoring: x² + 10x + 24 = 0

    x?x?x²?x?x24two numbers that multiply to 24and add to 10
    Answer

★ Challenge corner for fast finishers

What is the units (ones) digit of 3^34?

How did I do?

Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/8/quadratics

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

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