Download presentation

Presentation is loading. Please wait.

Published byAnnabelle Stanley Modified over 8 years ago

1
1.6 Shifting, Reflecting and Stretching Graphs How to vertical and horizontal shift To use reflections to graph Sketch a graph

2
Shifting (up and down) How is y = x 2 different from y – k = a(x – h) 2 y = a(x – h) 2 + k k shifts the graph up or down.

3
Shifting (right or left) How is y = x 2 different from y – k = a(x – h) 2 y = a(x – h) 2 + k h shifts the graph Left or Right.

4
Reflecting Over the x axis will change y to – y Over the y axis will change x to - x How does this effect f(x) = x 2 + 2

5
f(x) = x 2 + 2 Over the x axis where f(x) becomes – f(x) -f(x) = -(x 2 + 2) or –x 2 – 2 (0, 2) (0, - 2)

6
f(x) = x 2 + 2 Over the y axis where f(x) becomes f(- x) f(-x) = ( -x) 2 + 2 or f(x) = x 2 + 2 (0, 2) The graph and the equation are the same. What does this show?

7
Stretching (Nonrigid transformation) Shifting and reflection are rigid transformation; they move the graph without changing its shape. Lets look at the equationf(x) = ax 2

8
“a” will make the graph fat or skinny What would happen if a=4 in f(x) = ax 2 ? Would the graph become fat or skinny? FATSkinny

9
Skinny The values of f(x) become larger as “a” increase. f(x) = 4x 2 (- 3, 12) (3, 12) (-1, 4) (1, 4) (0, 0)

10
What would make the Graph Fat?

11
Where “a” is 0 < a < 1. (-2, 1)( 2, 1) (0, 0)

12
So lets look at the equation y = a(x – h) 2 + k h will move the graph Left or Right (must remember (x + 3) means h is – 3) k will move the graph up or down a will stretch the graph fat or skinny

13
Homework Page 64 – 68 #4, 11, 17, 27, 35, 43, 49, 57, 69, 83

14
Homework Page 64 – 68 #9, 13, 21, 31, 39, 45, 53, 65, 71, 81

Similar presentations

© 2023 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google