1. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 1 Chapter 9 Quadratic Equations and Functions

2. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 2 Quadratic Equations and Functions CHAPTER 9.1The Square Root Principle and Completing the Square 9.2Solving Quadratic Functions Using the Quadratic Formula 9.3Solving Equations That Are Quadratic in Form 9.4Graphing Quadratic Functions 9 Copyright © 2014, 2010, 2007 Pearson Education, Inc. 2

3. 3 Solving Quadratic Equations Using the Quadratic Formula 9.2 1.Solve quadratic equations using the quadratic formula.

4. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 4 Using the Quadratic Formula To solve a quadratic equation in the form ax 2 + bx + c = 0, where a 0, use the quadratic formula:

5. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 5 Example Solve. Solution The equation is in the form ax 2 + bx + c = 0, where a = 2, b = –7, and c = 3.

6. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 6 Example Solve. Solution First we need to write the equation in the form ax 2 + bx + c = 0. a = 1, b = –2, c = –11.

7. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 7 Example Solve. Solution First we need to write the equation in the form ax 2 + bx + c = 0. Notice that the radicand is 0, which causes this equation to have only one solution.

8. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 8 MethodWhen the Method is Beneficial 1. Factoring (Section 6.6)Use when the quadratic equation can be easily factored. 2. Square root principle (Section 9.1) Use when the quadratic equation can be easily written in the form 3. Completing the square (Section 9.1) Rarely the best method, but important for future topics. 4. Quadratic formula (Section 9.2) Use when factoring is not easy, or possible, with integer coefficients. Methods for Solving Quadratic Equations