1. Slide 6 - 1 Copyright © 2009 Pearson Education, Inc. 6.9 Continued Solving Quadratic Equations by Using Factoring and by Using the Quadratic Formula

2. Slide 6 - 2 Copyright © 2009 Pearson Education, Inc. Solving Quadratic Equations by Factoring Standard Form of a Quadratic Equation ax 2 + bx + c = 0, a  0 Zero-Factor Property If a b = 0, then a = 0 or b = 0.

3. Slide 6 - 3 Copyright © 2009 Pearson Education, Inc. To Solve a Quadratic Equation by Factoring Use the addition or subtraction property to make one side of the equation equal to 0. Factor the side of the equation not equal to 0. Use the zero-factor property to solve the equation.

4. Slide 6 - 4 Copyright © 2009 Pearson Education, Inc. Example: Solve by Factoring Solve 4x 2 + 17x  15 = 0. The solutions are  5 and ¾. or

5. Slide 6 - 5 Copyright © 2009 Pearson Education, Inc. Solve by factoring

6. Slide 6 - 6 Copyright © 2009 Pearson Education, Inc. Practice Problem: Solve by factoring

7. Slide 6 - 7 Copyright © 2009 Pearson Education, Inc. Quadratic Formula For a quadratic equation in standard form, ax 2 + bx + c = 0, a  0, the quadratic formula is

8. Slide 6 - 8 Copyright © 2009 Pearson Education, Inc. Example: Using the Quadratic Formula Solve the equation 3x 2 + 2x  7 = 0. a = 3, b = 2 and c =  7

9. Slide 6 - 9 Copyright © 2009 Pearson Education, Inc. Practice Problem: solve using the quadratic equation

10. Slide 6 - 10 Copyright © 2009 Pearson Education, Inc. Homework: P 360 # 35 – 77 eoo