16. g(x) =
9-3 Transformations of Quadratic Functions
Describe how the graph of each function is
2
related to the graph of f (x) = x .
8. g(x) = −10 + x
2
ANSWER: translated down
2
x +
ANSWER: compressed vertically, translated up
2
17. h(x) = 1.01x − 6.5
ANSWER: stretched vertically, translated down
Match each equation to its graph.
A
2
9. h(x) = −7 − x
ANSWER: reflected across the x-axis, translated down
2
10. g(x) = 2x + 8
ANSWER: stretched vertically, translated up
11. h(x) = 6 +
x
B
2
ANSWER: compressed vertically, translated up
12. g(x) = −5 −
x
2
C
ANSWER: reflected across the x-axis, stretched vertically,
translated down
13. h(x) = 3 +
x
2
D
ANSWER: stretched vertically, translated up
2
14. g(x) = 0.25x − 1.1
ANSWER: compressed vertically, translated down
2
15. h(x) = 1.35x + 2.6
E
ANSWER: stretched vertically, translated up
16. g(x) =
2
x +
ANSWER: compressed vertically, translated up
2
eSolutions
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= 1.01x
17. h(x)Manual
− 6.5 by Cognero
ANSWER: stretched vertically, translated down
F
Page 1
2
23. y = 3x + 2
ANSWER: E
9-3 Transformations of Quadratic Functions
F
24. SQUIRRELS A squirrel 12 feet above the ground
2
drops an acorn from a tree. The function h = −16t +
12 models the height of the acorn above the ground
in feet after t seconds. Graph the function and
compare this graph to the graph of its parent
function.
18. y =
ANSWER: The graph is stretched vertically, reflected across the
x-axis, and translated up.
2
x −4
ANSWER: C
2
19. y = − x − 4
ANSWER: A
20. y =
2
x +4
CCSS REGULARITY List the functions in
order from the most stretched vertically to the
least stretched vertically graph.
ANSWER: B
2
25. g(x) = 2x , h(x) =
x
2
2
21. y = −3x − 2
ANSWER: g(x), h(x)
ANSWER: F
2
2
26. g(x) = −3x , h(x) =
22. y = −x + 2
ANSWER: D
x
2
ANSWER: g(x), h(x)
2
23. y = 3x + 2
2
2
27. g(x) = −4x , h(x) = 6x , f (x) = 0.3x
ANSWER: E
2
ANSWER: h(x), g(x), f (x)
24. SQUIRRELS A squirrel 12 feet above the ground
2
2
2
28. g(x) = −x , h(x) =
ANSWER: The graph is stretched vertically, reflected across the
x-axis, and translated up.
29. ROCKS A rock falls from a cliff 300 feet above the
ground. Another rock falls from a cliff 700 feet
above the ground.
a. Write functions that model the height h of each
rock after t seconds.
b. If the rocks fall at the same time, how much Page 2
sooner will the first rock reach the ground?
eSolutions Manual - Powered by Cognero
x , f (x) = −4.5x
2
drops an acorn from a tree. The function h = −16t +
12 models the height of the acorn above the ground
in feet after t seconds. Graph the function and
compare this graph to the graph of its parent
function.
ANSWER: f(x), h(x), g(x)
2
28. g(x) = −x , h(x) =
2
x , f (x) = −4.5x
2
ANSWER: 9-3 Transformations
of Quadratic Functions
f(x), h(x), g(x)
29. ROCKS A rock falls from a cliff 300 feet above the
ground. Another rock falls from a cliff 700 feet
above the ground.
a. Write functions that model the height h of each
rock after t seconds.
b. If the rocks fall at the same time, how much
sooner will the first rock reach the ground?
ANSWER: 2
2
a. h = −16t + 300 and h = −16t + 700
b. about 2.3 seconds
30. SPRINKLERS The path of water from a sprinkler
can be modeled by quadratic functions. The following
functions model paths for three different sprinklers.
2
Sprinkler A: y = −0.35x + 3.5
2
Sprinkler B: y = −0.21x + 1.7
2
Sprinkler C: y = −0.08x + 2.4
a. Which sprinkler will send water the farthest?
Explain.
b. Which sprinkler will send water the highest?
Explain.
c. Which sprinkler will produce the narrowest path?
Explain.
ANSWER: a. Sprinkler C because the graph is compressed
vertically the most.
b. Sprinkler A because it is translated up the most.
c. Sprinkler A because it is expanded the least.
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