The document introduces two methods for solving quadratic equations - factoring and graphing. It provides examples of equations that cannot be solved using these methods. It then introduces the quadratic formula as the method to use for equations that cannot be factored or graphed easily. It walks through identifying the a, b, and c coefficients needed for the quadratic formula. It provides examples of using the formula and encourages practicing with a worksheet.

1. QUADRATIC FORMULA

2. 2 WAYS TO SOLVE QUADRATIC EQUATIONS Factoring (x )(x ) = 0 Graphing But, what if factoring and graphing are not possible??

3. EXAMPLE #1 2x 2 – 4x – 3 = 0 * can not be factored: (2x )(x ) * can not easily be graphed for a solution: X 2x 2 – 4x – 3 = 0 0 -3 1 -5 -1 -1

4. EXAMPLE #2 x 2 – 4x – 8 = 0 * can not be factored: (x )(x ) * can not easily be graphed for a solution: WHAT DO WE DO?? X x 2 – 4x – 8 = 0 0 -8 1 -11 -1 -3

5. We use the QUADRATIC FORMULA

6. THE DIFFERENT PARTS OF THE QUADRATIC FORMULA Standard Form of a Quadratic Equation: ax 2 + bx + c = 0 Let’s look at Example #1 to identify the different parts: 2x 2 – 4x – 3 = 0 ax 2 + bx + c = 0 a = 2 b = -4 c = -3

7. LET’S DO EXAMPLE #1 a = 2 b = -4 c = -3 2x 2 – 4x – 3 = 0

8. NOW YOU TRY A PROBLEM a = 2 b = -1 c = -6 2x 2 – x – 6 = 0

9. SOME PROBLEMS REQUIRE US TO REWRITE THEM IN STANDARD FORM FIRST a = 1 b = -4 c = -8 x 2 – 4x = 8 x 2 – 4x - 8 = 0 Rewrite in standard form

10. NOW YOU TRY A PROBLEM a = 2 b = 5 c = -10 2x 2 = -5x +10 2x 2 + 5x – 10 Rewrite in standard form

11. HOW ABOUT YOU TRY SOME PROBLEMS ON YOUR OWN NOW… Try the QUADRATIC FORMULA WORKSHEET and then see me to check your answers

12. LET’S LISTEN TO THAT SONG AGAIN!

13. ANY QUESTIONS???

14. SOME VERSIONS OF THE QUADRATIC FORMULA SONG: http://www.youtube.com/watch?v=U7q5fgGyqxk http://www.youtube.com/watch?v=D_0vgqi7fU4