Graphs of Quadratic Functions

Contributed by:

Sharp Tutor Mon, Jan 17, 2022 07:32 PM UTC

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.

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

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

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

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 - 4

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

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

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

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

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

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 - 10

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 - 11

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 - 12

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 - 16

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 - 17

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 - 18

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.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 10.5 - 19

Book a Trial Class

Download