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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

#### 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

Simplify.

### 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

10. 80 x 2 – 16 x – 32 = 0

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

12. x 2 + 10 x + 25 = 0

#### Solutions

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