Vertical Stretch:
When there is a 2y in the equation then there is a vertical
stretch of 1/2 (gets fatter) .
When there is a ½ y in the equation then there is a vertical
stretch of 2 and the graph gets skinny.
The vertical stretch factor is the reciprocal of the
coefficient of y.
Extra Practice: x value from -4 to 4
a) 5y = x2
­ equation
b) -2y = x2
­graph
c) 1/2y = -x2
­mapping notation
d) 1/4y = x2
­description in words 1
Re­writing Functions: Re­write the following functions to get y alone. 1. 3y = x2
2. 1/2y = x2 ­ 2
3. 7y = x2 + 4 4. y ­ 2 = x2
5. y + 4 = x2 6. ­3(y + 2) = x2
7. ­1/10y = x2
8. ­2y ­ 4 = x2
2
no reflection
vertical stretch of 1/5 3
reflection strech factor 1/2 4
reflection no vertical translation
no horizontal translation
stretch factor of 2 5
Mapping notation (x, y) (x, 4y) Description in words:
no reflection
vertical stretch of 4 6
Practice: y = x2 + 1
x
y
Graph 7
y = x2 + 1 no reflection
no vertical stretch vertical translation of + 1 Mapping Notation (x , y) (x, y + 1)
8
y +2 = x2
x
y
No reflection
vertical translation of ­2 Description in Words
no vertical stretch. Mapping Mapping Notation Notation
(x , y) (x, y ­ 2)
9
y ­ 3 = x2
x
y
No reflection
vertical translation of +3 Description in Words
no horizontal translation
no stretch factor. Mapping Mapping Notation
Notation (x , y) (x, y + 3)
10
When there is a y + 2 in the equation then
there is a vertical translation of ____ units _____.
When there is a y - 3 in the equation then
there is a vertical translation of ____ units _____.
11
Mapping Notation
Equation
Description in Words Graph
no reflection
vertical stretch of 4
no vertical translation
1/4y = x2
(x, y) (x, 4y) y = 2x2 +3
no reflection
vertical stretch of 2
(x, y) (x, 2y +3) vertical translation
of 3 reflection
2 (x, y) (x, ­5y ­3) vertical strech of 5
y +3 = ­5x
1/2y ­ 1 = x
vertical translation of ­3
2
no reflection
vertical strech of 2
(x, y) (x, 2y +1) vertical translation of ­1
12