Quadratic Equations, Inequalities, and Functions

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Presentation transcript:

Quadratic Equations, Inequalities, and Functions Chapter 10 Quadratic Equations, Inequalities, and Functions

Graphs of Quadratic Functions 10.5 Graphs of Quadratic Functions

10.5 Graphs of Quadratic Functions Objectives Graph a quadratic function. Graph parabolas with horizontal and vertical shifts. Use the coefficient of x2 to predict the shape and direction in which a parabola opens. Find a quadratic function to model data. Copyright © 2010 Pearson Education, Inc. All rights reserved.

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

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

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 Copyright © 2010 Pearson Education, Inc. All rights reserved.

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

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

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

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

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. Copyright © 2010 Pearson Education, Inc. All rights reserved.

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

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

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

10.5 Graphs of Quadratic Functions General Principles of Parabolas (4, -7) Shifted right 4 units and down 7 units. Narrower than f (x) = x2. Copyright © 2010 Pearson Education, Inc. All rights reserved.

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. Copyright © 2010 Pearson Education, Inc. All rights reserved.

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

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. Copyright © 2010 Pearson Education, Inc. All rights reserved.