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The Quadratic Formula Practice Problems

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By — McGraw-Hill Professional
Updated on Sep 27, 2011

The Quadratic Formula Practice Problems

Set 1: Introduction to the Quadratic Formula - The Quadratic Formula in Practice

To review The Quadratic Formula, go to The Quadratic Formuls Help

Practice

Identify a , b , and c for ax 2 + bx + c = 0.

  1. 2 x 2 + 9 x + 3 = 0
  2. – 3 x 2 + x + 5 = 0
  3. x 2x – 6 = 0
  4. x 2 – 9 = 0
  5. 2 x 2 = 32
  6. x 2 + x = 0
  7. x 2x = 0
  8. 9 x 2 = 10 x
  9. 8 x 2 + 20 x = 9
  10. 4 x – 5 – 3 x 2 = 0

Solutions

  1. 2 x 2 + 9 x + 3 = 0 a = 2 b = 9 c = 3
  2. –3 x 2 + x + 5 = 0 a = – 3 b = 1 c = 5
  3. x 2x – 6 = 0 a = 1 b = – 1 c = – 6
  4. x 2 – 9 = 0 a = 1 b = 0 c = – 9
  5. 2 x 2 = 32 Rewritten: 2 x 2 – 32 = 0 a = 2 b = 0 c = – 32
  6. x 2 + x = 0 a = 1 b = 1 c = 0
  7. x 2x = 0 a = 1 b = –1 c = 0
  8. 9 x 2 = 10 x Rewritten: 9 x 2 – 10 x = 0
  9. a = 9 b = –10 c = 0

  10. 8 x 2 + 20 x = 9 Rewritten: 8 x 2 + 20 x – 9 = 0
  11. a = 8 b = 20 c = – 9

  12. 4 x – 5 – 3 x 2 = 0 Rewritten: – 3 x 2 + 4 x – 5 = 0
  13. a = –3 b = 4 c = – 5

Set 2: Simplifying the Quadratic Formula

Sometimes the solutions to a quadratic equation need to be simplified. To review this concept, go to The Quadratic Formula Help

Practice

Simplify.

The Quadratic Formula

Solutions

The Quadratic Formula Solutions

The Quadratic Formula Solutions

Set 3: Solving Equations Using the Quadratic Formula

To review solving quadratic equations using the formula, go to The Quadratic Formula Help

Practice

1. x 2 – 5 x + 3 = 0

2. 4 x 2 + x – 6 = 0

3. 7 x 2 + 3 x = 2

4. 2 x 2 = 9

5. – 3 x 2 + 4 x + 1 = 0

6. 9 x 2 – x = 10

7. 10 x 2 – 5 x = 0

8. 0.1 x 2 – 0.11 x – 1 = 0

The Quadratic Formula Solutions

10. 80 x 2 – 16 x – 32 = 0

11. 18 x 2 + 39 x + 20 = 0

12. x 2 + 10 x + 25 = 0

Solutions

The Quadratic Formula Solutions

The Quadratic Formula Solutions

The Quadratic Formula Solutions

The Quadratic Formula Solutions

The Quadratic Formula Solutions

The Quadratic Formula Solutions

The Quadratic Formula Solutions

The Quadratic Formula Solutions

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