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

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Presentation transcript:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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