Translating Parabolas

1
Translating Parabolas
ALGEBRA 2 LESSON 5-3
(For help, go to Lesson2-6.)
Identify the parent function of each function.
Then graph the function by translating the parent
function.
1. y x 2 2. y 3x 2 3. y x 1
1 4. y 2x, 2 units down 5. y x, 4 units
up, 1 unit right
Write an equation for each translation.
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2
Translating Parabolas
ALGEBRA 2 LESSON 5-3
Solutions
1. y x 2 parent function y
x translate 2 units up 3. y x 1
1 parent function y x translate 2 unit left
and one unit down
2. y 3x 2 parent function y
3x translate 2 units up
4. y 2x, 2 units down y 2x 2 5. y x, 4
units up and 1 unit right y (x 1) 4, or y
x 3
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Translating Parabolas
ALGEBRA 2 LESSON 5-3
2 3
Graph y (x 1)2 2.
You can graph it by translating the parent
function or by finding the vertex and the axis of
symmetry.
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Translating Parabolas
ALGEBRA 2 LESSON 5-3
Write the equation of the parabola shown below.
y a(x h)2 k Use the vertex form.
y a(x 2)2 5 Substitute h 2 and k 5.
3 a(0 2)2 5 Substitute (0, 3).
2 4a Simplify.
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5
Translating Parabolas
ALGEBRA 2 LESSON 5-3
A long strip of colored paper is attached as a
party decoration at exactly opposite corners of
the back wall of a rectangular party room. The
strip approximates a parabola with equation y
0.008(x 25)2 10. The bottom left corner of
the back wall is the origin and x and y are
measured in feet. How far apart are the side
walls? How high are they?
The function is in vertex form. Since h 25 and
k 10, the vertex is at (25, 10).
The vertex is halfway between the two corners of
the wall, so the width of the wall is 2(25 ft)
50 ft.
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Translating Parabolas
ALGEBRA 2 LESSON 5-3
(continued)
To find the walls height, find y for x 0.
The wall is 50 ft long and 15 ft high.
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7
Translating Parabolas
ALGEBRA 2 LESSON 5-3
Write y 7x2 70x 169 in vertex form.
The vertex is at (5, 6).
The vertex form of the function is y 7(x 5)2
6.
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