NAME
DATE
9-3
PERIOD
Practice
Transformations of Quadratic Functions
Describe how the graph of each function is related to the graph of f(x) = x2.
2
2. g(x) = - −
+ x2
1. g(x) = (10 + x)2
3. g(x) = 9 - x2
5
Translation of f(x) = x2
to the left 10 units.
Translation of f(x) = x2
2
down −
unit.
5
3 2
1
5. g(x) = - −
x -−
4. g(x) = 2x2 + 2
4
Stretch of f(x) = x2
narrower than the
graph of f(x) = x2
translated up 2 units.
Reflection of
f(x) = x2 across the
x-axis translated up
9 units.
6. g(x) = -3(x + 4)2
2
Compression of f(x) = x2
wider than the graph of
f(x) = x2, reflected over
the x-axis, translated
1
down −
unit.
Stretch of
f(x) = x2 narrower
than the graph of
f(x) = x2, reflected
over the x-axis
translated to the left
4 units.
2
Match each equation to its graph.
y
A.
y
B.
A
7. y = -3x2 - 1
0
1 2
8. y = −
x -1
3
x
x
0
C
B
9. y = 3x2 + 1
List the functions in order from the most vertically stretched to the least
vertically stretched graph.
1 2
x , h(x) = -2x2
10. f(x) = 3x2, g(x) = −
f(x), h(x), g(x)
2
1 2
1 2
11. f(x) = −
x , g(x) = - −
x , h(x) = 4x2
2
h(x), f(x), g(x)
6
12. PARACHUTING Two parachutists jump at the same time from two different planes as
part of an aerial show. The height h1 of the first parachutist in feet after t seconds is
modeled by the function h1 = -16t2 + 5000. The height h2 of the second parachutist in
feet after t seconds is modeled by the function h2 = -16t2 + 4000.
a. What is the parent function of the two functions given? h = t2
b. Describe the transformations needed to obtain the graph of h1 from the parent
function. Stretch of y = x2 narrower than the graph of f(x) = x2, reflected
over the x-axis, translated up 5000 units.
c. Which parachutist will reach the ground first? the second parachutist
Chapter 9
20
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
x
0
y
C.