1. Solving Quadratic Equations by Factoring 6.6 1.Use the zero-factor theorem to solve equations containing expressions in factored form. 2.Solve quadratic equations by factoring. 4.Use the Pythagorean theorem to solve problems. 3.Solve problems involving quadratic equations.

2. Factors: xy2 factors x(x + 1)2 factors (x + 2)(x - 3)2 factors What’s the difference? Expression: factorEquation: solve expressions that are multiplied

3. Quadratic equation in one variable: An equation that can be written in the form ax 2 + bx + c = 0, where a, b, and c are all real numbers and a  0.

4. Zero-Factor Theorem If a and b are real numbers and ab = 0, then a = 0 or b = 0. Only works because of the property of 0!

5. Solving Quadratic Equations Using Factoring 1. Write in standard form. (Set = 0.) ax 2 + bx + c = 0 2. Factor. 3. Use the zero-factor theorem to solve.

6. Solve: 1. Write in standard form. (Set = 0.) 2. Factor.

7. Solve: 3. Use the zero-factor theorem to solve. 1. Write in standard form. (Set = 0.) 2. Factor.

8. Solve: 3. Use the zero-factor theorem to solve. 1. Write in standard form. (Set = 0.) 2. Factor.

9. Solve: 3. Use the zero-factor theorem to solve. 1. Write in standard form. (Set = 0.) 2. Factor.

10. Solve: 3. Use the zero-factor theorem to solve. 1. Write in standard form. (Set = 0.) 2. Factor.

11. Copyright © 2011 Pearson Education, Inc. The Pythagorean Theorem Given a right triangle, then a 2 + b 2 = c 2. c (hypotenuse) b (leg) a (leg)

12. Find the length of the missing side. a 2 + b 2 = c 2 15 2 + 36 2 = c 2 Substitute. 225 + 1296 = c 2 Simplify exponential forms. 1521 = c 2 Add. c 2 – 1521 = 0 Standard form. (c – 39)(c + 39) = 0 Factor. c – 39 = 0 or c + 39 = 0 c = 39 or c = –39 Length cannot be negative. Copyright © 2011 Pearson Education, Inc. ? 36 15

13. Slide 6- 13 Copyright © 2011 Pearson Education, Inc. Solve. x 2 = 6x – 8 a) 2 and 4 b) 2 and  4 c)  2 and 4 d) 1 and  8 6.6

14. Slide 6- 14 Copyright © 2011 Pearson Education, Inc. Solve. x 2 = 6x – 8 a) 2 and 4 b) 2 and  4 c)  2 and 4 d) 1 and  8 6.6

15. Slide 6- 15 Copyright © 2011 Pearson Education, Inc. Find the length of the hypotenuse. a) 15 b) 46 c) 50 d) 62 ? 48 14 6.6

16. Slide 6- 16 Copyright © 2011 Pearson Education, Inc. Find the length of the hypotenuse. a) 15 b) 46 c) 50 d) 62 ? 48 14 6.6