1. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 10.5 - 1

2. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 10.5 - 2 Quadratic Equations, Inequalities, and Functions Chapter 10

3. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 10.5 - 3 10.5 Graphs of Quadratic Functions

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 4 10.5 Graphs of Quadratic Functions Objectives 1.Graph a quadratic function. 2.Graph parabolas with horizontal and vertical shifts. 3.Use the coefficient of x 2 to predict the shape and direction in which a parabola opens. 4.Find a quadratic function to model data.

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 5 10.5 Graphs of Quadratic Functions Graph a Quadratic Function

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 6 10.5 Graphs of Quadratic Functions Graph Parabolas with Vertical Shifts

7. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 7 10.5 Graphs of Quadratic Functions Graph Parabolas with Vertical Shifts k > 0 produces shift up k units k < 0 produces shift down k units

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 8 10.5 Graphs of Quadratic Functions Graph Parabolas with Horizontal Shifts

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 9 10.5 Graphs of Quadratic Functions Graph Parabolas with Horizontal Shifts h > 0 produces shift right h units h < 0 produces shift left h units

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 10 10.5 Graphs of Quadratic Functions Graph Parabolas with Horizontal and Vertical Shifts

11. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 11 10.5 Graphs of Quadratic Functions Graph Parabolas with Horizontal and Vertical Shifts

12. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 12 10.5 Graphs of Quadratic Functions Graph Parabolas with Horizontal and Vertical Shifts Since h < 0, there is a shift to the left, and since k < 0, there is a shift down.

13. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 13 10.5 Graphs of Quadratic Functions Graph Parabolas with Horizontal and Vertical Shifts Axis of symmetry Vertex

14. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 14 10.5 Graphs of Quadratic Functions General Principles of Parabolas

15. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 15 10.5 Graphs of Quadratic Functions General Principles of Parabolas

16. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 16 10.5 Graphs of Quadratic Functions General Principles of Parabolas (4, -7) Shifted right 4 units and down 7 units. Narrower than f (x) = x 2.

17. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 17 10.5 Graphs of Quadratic Functions Finding a Quadratic Model The following table shows the higher-order multiple birth rates in the United States since 1971. At the right is a scatter diagram of these points.

18. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 18 10.5 Graphs of Quadratic Functions Finding a Quadratic Model We will select three arbitrary ordered pairs to construct our model.

19. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 19 10.5 Graphs of Quadratic Functions Finding a Quadratic Model Selecting three representative ordered pairs, we can write a system of three equations. Solving these equations using technology, we determine Choosing different ordered pairs would result in a different model.