1. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 10.1 - 1

2. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 10.1 - 2 Quadratic Equations, Inequalities, and Functions Chapter 10

3. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 10.1 - 3 10.1 The Square Root Property and Completing the Square

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 4 10.1 The Square Root Property and Completing theSquare Objectives 1.Review the zero-factor property. 2.Learn the square root property. 3.Solve quadratic equations of the form ( a x + b) 2 = c by using the square root property. 4.Solve quadratic equations by completing the square. 5.Solve quadratic equations with nonreal complex solutions.

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 5 10.1 The Square Root Property and Completing the Square In Section 7.5, we defined a quadratic equation as follows: Example: We then used factoring and the zero-factor property to solve the equation Solving: Quadratic Equations and the Zero-Factor Property

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 6 10.1 The Square Root Property and Completing the Square Not all quadratic equations are factorable over the integers. We will now examine other methods for solving quadratic equations regardless of whether they can be factored. We base these methods on the following property. The Square Root Property

7. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 7 10.1 The Square Root Property and Completing the Square Solve each equation. Using the Square Root Property

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 8 10.1 The Square Root Property and Completing the Square Each solution can be checked by substituting back into the original equation. Using the Square Root Property

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 9 10.1 The Square Root Property and Completing the Square Solving Quadratic Equations of the Form ( a x + b) 2 = c Solve.

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 10 10.1 The Square Root Property and Completing the Square Solving Quadratic Equations of the Form ( a x + b) 2 = c Check.

11. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 11 10.1 The Square Root Property and Completing the Square We can use the observations of the previous cases to build our own perfect square trinomials and, in doing so, solve some quadratic equations. Solve Quadratic Equations by Completing the Square

12. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 12 10.1 The Square Root Property and Completing the Square Solve Quadratic Equations by Completing the Square Cont’d from previous

13. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 13 10.1 The Square Root Property and Completing the Square Solve Quadratic Equations by Completing the Square Solving:

14. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 14 10.1 The Square Root Property and Completing the Square Solve Quadratic Equations by Completing the Square

15. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 15 10.1 The Square Root Property and Completing the Square Completing the Square with a = 1

16. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 16 10.1 The Square Root Property and Completing the Square Completing the Square with

17. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 17 10.1 The Square Root Property and Completing the Square Quadratic Equations with Nonreal Complex Solutions Solve each equation.

18. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.1 - 18 10.1 The Square Root Property and Completing the Square Quadratic Equations with Nonreal Complex Solutions Solve.