**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.

- 2
*x*^{2}+ 9*x*+ 3 = 0 - – 3
*x*^{2}+*x*+ 5 = 0 *x*^{2}–*x*– 6 = 0*x*^{2}– 9 = 0- 2
*x*^{2}= 32 *x*^{2}+*x*= 0*x*^{2}–*x*= 0- 9
*x*^{2}= 10*x* - 8
*x*^{2}+ 20*x*= 9 - 4
*x*– 5 – 3*x*^{2}= 0

**Solutions**

- 2
*x*^{2}+ 9*x*+ 3 = 0*a*= 2*b*= 9*c*= 3 - –3
*x*^{2}+*x*+ 5 = 0*a*= – 3*b*= 1*c*= 5 *x*^{2}–*x*– 6 = 0*a*= 1*b*= – 1*c*= – 6*x*^{2}– 9 = 0*a*= 1*b*= 0*c*= – 9- 2
*x*^{2}= 32 Rewritten: 2*x*^{2}– 32 = 0*a*= 2*b*= 0*c*= – 32 *x*^{2}+*x*= 0*a*= 1*b*= 1*c*= 0*x*^{2}–*x*= 0*a*= 1*b*= –1*c*= 0- 9
*x*^{2}= 10*x*Rewritten: 9*x*^{2}– 10*x*= 0 - 8
*x*^{2}+ 20*x*= 9 Rewritten: 8*x*^{2}+ 20*x*– 9 = 0 - 4
*x*– 5 – 3*x*^{2}= 0 Rewritten: – 3*x*^{2}+ 4*x*– 5 = 0

*a* = 9 *b* = –10 *c* = 0

*a* = 8 *b* = 20 *c* = – 9

*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.

**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

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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