1. The Square Root Principle and Completing the Square 11.1 1.Use the square root principle to solve quadratic equations. 2.Solve quadratic equations by completing the square.

2. Solve: Quadratic Equation Set = 0 Two solutions

3. The Square Root Principle If, then. Isolated perfect square. No middle term. Always 2 solutions.

4. Solve: 4∙15 5 1 3 1 What do you see? Fractions Perfect square – no m term

5. Slide 11- 5 Copyright © 2011 Pearson Education, Inc. Solve. a) b) c) d) 11.1

6. Slide 11- 6 Copyright © 2011 Pearson Education, Inc. Solve. a) b) c) d) 11.1

7. Solve:

8. Solve:

9. Solve: 4∙7

10. 2 rational solutions 2 irrational solutions 2 non-real imaginary solutions

11. Slide 11- 11 Copyright © 2011 Pearson Education, Inc. Solve. a) b) c) d) 11.1

12. Slide 11- 12 Copyright © 2011 Pearson Education, Inc. Solve. a) b) c) d) 11.1

13. Completing the Square + 3 + 9 - 7 + 49 ½ squared ½ ½ ½ Coefficient of the squared term must be1.

14. Solve: ½ + 5 squared + 25 13 2 irrational solutions Coefficient of squared term is 1.

15. Solve: ½ 3 2 squared 9494 2 irrational solutions Coefficient of squared term is NOT 1. 9494 + 9494 + 10 4 =

16. Solve: ½ squared 2 rational solutions Coefficient of squared term is NOT 1. Factorable!

17. Slide 11- 17 Copyright © 2011 Pearson Education, Inc. Solve by completing the square. a) b) c) d) 11.1

18. Slide 11- 18 Copyright © 2011 Pearson Education, Inc. Solve by completing the square. a) b) c) d) 11.1