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WorksheetsTransformations of Quadratic Functions
Total questions: 25
Worksheet time: 52mins
Name
Class
Date
1.
Which transformation maps the graph of
f(x) = x2 to the graph of g(x) = (x + 4)2?
f(x) = x2 to the graph of g(x) = (x + 4)2?
a)
a translation shifting f(x) 4 units up
b)
a translation shifting f(x) 4 units down
c)
a translation shifting f(x) 4 units to the left
d)
a translation shifting f(x) 4 units to the right
2.
Which transformation will occur if f(x) = x2 is replaced with 2⋅f(x)?
a)
Wider
b)
Narrower
c)
Vertical translation up by 2 units.
d)
Reflection across the x-axis.
3.
Which transformation will occur if f(x) = x2 is replaced with f(x) + 2?
a)
Translation left 2 units
b)
Narrower
c)
Vertical translation up by 2 units.
d)
Reflection across the x-axis.
4.
The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x + 2) , what is the vertex of g(x)?
a)
(-2, 5)
b)
(-6, 5)
c)
(-4, 3)
d)
(-4, 7)
5.
f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)
a)
g(x)=f(x + 3)
b)
g(x)=f(x - 3)
c)
g(x)=f(x) + 3
d)
g(x)=f(x) - 2
6.
The vertex of the quadratic function f(x) = -2x2 + 4x + 3 if (1, 5). If g(x) = f(x - 2), what is the vertex of g(x)
a)
(1, 3)
b)
(1, 7)
c)
(-1, 5)
d)
(3, 5)
7.
How did we transform from the parent function?
g(x) = -1/5(x - 1)2 + 7
g(x) = -1/5(x - 1)2 + 7
a)
reflection, vertical compression, horizontal right, vertical up
b)
vertical compression, horizontal shift left, vertical shift up
c)
reflection, horizontal shift right, vertical shift down
d)
no changes were made to y = x2
8.
Which quadratic function is represented by the graph?
a)
y = 2(x - 4)2 + 5
b)
y = 2(x + 4)2 + 5
c)
y = -2(x - 4)2 + 5
d)
y = -2(x + 4)2 + 5
9.
If the blue graph is
f(x) = x2
then the red must be...
f(x) = x2
then the red must be...
a)
g(x) = x2 - 5
b)
g(x) = x2 + 5
c)
g(x) = (x - 5)2
d)
g(x) = (x + 5)2
10.
What transformations occurred to get f(x), the red graph, to become g(x), the blue graph?
a)
horizontal shift down and vertical shift left
b)
horizontal shift left and vertical shift down
c)
horizontal shift right and vertical shift up
d)
horizontal shift up and vertical shift right
11.
What transformations have occurred?
a)
Right 2 and up 2
b)
Left 2 and up 2
c)
Right 2 and down 2
d)
Left 2 and down 2
12.
In the graph of the function y=x², which describes a vertical shift in the parent function up 5 units?
a)
y = x2 - 5
b)
y = x2 + 5
c)
y = (x - 5)2
d)
y = (x + 5)2
13.
Match the equation to its description.
a)
Right 2 and up 2
b)
Left 2 and up 2
c)
Right 2 and down 2
d)
Left 2 and down 2
14.
Which of the following is the correct equation for the given graph?
a)
f(x) = (x - 2)2 - 1
b)
f(x) = (x + 2)2 - 1
c)
f(x) = -(x + 2)2 - 1
d)
f(x) = -(x - 2)2 - 1
15.
In the equation f(x)=5(x+3)2-10 what does the 5 do?
a)
Vertical stretch by 5
b)
Horizontal compress by 5
c)
Reflect
d)
Move up 5
16.
In the equation f(x)=5(x+3)2-10 what effect does the 5 do when compared to the parent function?
a)
Vertical stretch by a factor of 5
b)
Vertical compress by a factor of 5
c)
Reflect over x-axis
d)
Vertical shift up 5 units
17.
What is the equation of the quadratic function obtained from horizontally shifting the parent function 17 units left and then reflecting across the x-axis?
a)
f(x)= -x2-17
b)
f(x)= -(x-17)2
c)
f(x)= -(x+17)2
d)
f(x)= -x2+17
18.
What would the equation for the new quadratic function be if it was horizontally shifted right 1 unit from the function f(x)=x2+4?
a)
g(x)=x2+5
b)
g(x)=(x+1)2+4
c)
g(x)=(x-1)2+4
d)
g(x)=x2+3
19.
Which quadratic function is represented by the graph?
a)
y = 2(x - 4)2 + 5
b)
y = 2(x + 4)2 + 5
c)
y = -2(x - 4)2 + 5
d)
y = -2(x + 4)2 + 5
20.
Which transformation maps the graph of
f(x) = x2 to the graph of g(x) = (x + 4)2?
f(x) = x2 to the graph of g(x) = (x + 4)2?
a)
a reflection across the line x = -4
b)
a reflection across the line y = -4
c)
a translation shifting f(x) 4 units to the left
d)
a translation shifting f(x) 4 units to the right
21.
Pablo throws a ball with a path of
h = -5(t - 2)2.
Maria throws a ball with a path of
h = -5(t - 2)2 + 10.
Which description is reasonable for the difference in the two equations?
h = -5(t - 2)2.
Maria throws a ball with a path of
h = -5(t - 2)2 + 10.
Which description is reasonable for the difference in the two equations?
a)
Maria throws the ball 10 times harder than Pablo does.
b)
Maria starts her ball at a height 10 feet higher than Pablo does.
c)
Pablo throws the ball 10 times harder than Maria does.
d)
Pablo starts his ball at a height 10 feet higher than Maria does.
22.
Match the equation to its description.
a)
Reflected over x and up 4
b)
Reflected over x and down 4
c)
Reflected over x and right 4
d)
Reflected over x and left 4
23.
Which list orders the quadratic functions from narrowest to widest?
a)
y = x2
y = 4x2
y = 2x2 - 2
y = 0.5 x2
y = 4x2
y = 2x2 - 2
y = 0.5 x2
b)
y = 0.5 x2
y = x2
y = 2x2 - 2
y = 4x2
y = x2
y = 2x2 - 2
y = 4x2
c)
y = 4x2
y = 2x2 - 2
y = x2
y = 0.5 x2
y = 2x2 - 2
y = x2
y = 0.5 x2
d)
y = 2x2 - 2
y = 4x2
y = 0.5x2
y = x2
y = 4x2
y = 0.5x2
y = x2
24.
What is the vertical shift of this equation?
f(x) = -(x + 3)2 - 5
f(x) = -(x + 3)2 - 5
a)
left 5
b)
right 5
c)
up 5
d)
down 5
25.
Does the graph of this equation open up or down?
f(x) = -(x + 3)2 - 5
f(x) = -(x + 3)2 - 5
a)
up
b)
down
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