Download 1.6 Shifting, Reflecting and Stretching Graphs

1.6 Shifting,
Reflecting and
Stretching Graphs
How to vertical and horizontal
shift To use reflections to graph
Sketch a graph
Shifting
(up and down)
How is y = x2 different
from y – k = a(x – h)2
y = a(x – h)2 + k
k shifts the graph
up or down.
Shifting
(right or left)
How is y = x2 different
from y – k = a(x – h)2
y = a(x – h)2 + k
h shifts the graph
Left or Right.
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) = x2 + 2
f(x) = x2 + 2
Over the x axis where f(x) becomes – f(x)
-f(x) = -(x2 + 2) or
–x 2 – 2
(0, 2)
(0, - 2)
f(x) = x2 + 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?
Stretching (Nonrigid transformation)
Shifting and reflection are rigid
transformation; they move the graph
without changing its shape.
Lets look at the equation
f(x) = ax 2
“a” will make the graph fat or skinny
What would happen if a=4 in f(x) = ax2?
Would the graph become fat or skinny?
FAT
Skinny
Skinny
The values of f(x) become larger as “a”
increase.
f(x) = 4x2
(- 3, 12)
(-1 , 4)
(3, 12)
(1, 4)
(0, 0)
What would make the Graph Fat?
What would make the Graph Fat?
1 2
Where “a” is 0 < a < 1. f ( x)  4 x
(-2, 1)
( 2, 1)
(0, 0)
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
Homework
Page 64 – 68
#4, 11, 17, 27, 35, 43, 49, 57, 69, 83
Homework
Page 64 – 68
#9, 13, 21, 31, 39, 45, 53, 65, 71, 81