1. 9.5 Solving by Factoring Algebra 14.0, 23.0

2. Predicting with Evidence What are the zeros for y = x 2 – x – 6? Now factor x 2 – x – 6 = 0 and solve. What do you notice about the graph and our factored solutions? What does this mean?

3. Main Idea For the rest of the chapter, we are going to learn different methods to solve a quadratic equation, besides graphing. Instead of graphing a parabola to find the zeros, we are going to learn ways to find the zeros, which are solutions. Today, we are going to use our chapter 8 skills to factor a quadratic equation. By breaking it down, we can find the zeros!

4. Zero Product Property Zero Product Property: if the product equals zero, then one of the values must equal zero. This property helps to find our ZEROS. Meaning: Our quadratic equation must equal 0 in order to find the zeros by solving.

5. Ex 1-Using the Zero Product Property These quadratic equations are already factored, so finish by setting each factor equal to 0 and solve.

6. Practice 1

7. Example 2: Solving by Factoring Solving by factoring: 1)Write the quadratic equation in standard form: y = ax 2 + bx + c OR ax 2 + bx + c = 0 2)Factor the quadratic equation (chapter 8) 3)Use the Zero Product Property to set each factor to 0 and solve. The answers are your zeros on the graph!

8. Ex 2- Solving Quadratic Equations By Factoring

10. Practice 2

11. Ex 3 Sports Application Same steps: 1)Write in standard form 2)Factor 3)Solve each factor to find the zeros!

12. Practice 3

13. Review What are you trying to find when you graph or solve quadratic equations? What is the zero product property? How does it help you solve? How do you know if your solutions are correct?