The Inverse Of A Quadratic Functions Worksheet
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83.3
The Inverse of a Quadratic
Function
YOU WILL NEED
GOAL
graph paper
•
Determine the inverse of a quadratic function, given different
ruler
•
representations.
•
graphing calculator
INVESTIGATE the Math
2
Suzanne needs to make a box in the shape of a cube. She has 864 cm
of cardboard
to use. She wants to use all of the material provided.
?
How long will each side of Suzanne’s box be?
Copy and complete this table.
A.
Cube Side Length (cm)
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3
4
5
6
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8
9
10
2
Area of Each Face (cm
)
1
4
2
Surface Area (cm
)
6
24
Draw a graph of surface area versus side length. What type of function is this?
B.
Explain how you know.
Determine the equation that represents the cube’s surface area as a function of
C.
its side length. Use function notation and state the domain and range.
How would you calculate the inverse of this function to describe the side
D.
length of the cube if you know its surface area?
Make a table of values for the inverse of the surface area function.
E.
Draw a graph of the inverse. Compare the graph of the inverse with the
F.
original graph. Is the inverse a function? Explain.
State the domain and range of the inverse.
G.
Write the equation that represents the cube’s side length for a given
H.
surface area.
Use your equation from part H to determine the largest cube Suzanne will be
I.
able to construct.
Reflecting
How are the surface area function and its inverse related
J.
a) in the table of values?
b) in their graphs?
c) in their domains and ranges?
155
Chapter 3 Quadratic Functions
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