19
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 10.5 - 1
| Date post: | 19-Jan-2016 |
| Category: |
Documents |
| Upload: | hannah-greene |
| View: | 217 times |
| Download: | 0 times |
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 10.5 - 1
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 10.5 - 2
Quadratic Equations, Inequalities,
and Functions
Chapter 10
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 10.5 - 3
10.5
Graphs of Quadratic Functions
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 x2 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 10.5 - 5
10.5 Graphs of Quadratic Functions
Graph a Quadratic Function
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 6
10.5 Graphs of Quadratic Functions
Graph Parabolas with Vertical Shifts
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
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 8
10.5 Graphs of Quadratic Functions
Graph Parabolas with Horizontal Shifts
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
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
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
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.
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
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 14
10.5 Graphs of Quadratic Functions
General Principles of Parabolas
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 15
10.5 Graphs of Quadratic Functions
General Principles of Parabolas
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) = x2.
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.
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.
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.
