Algebra 2
HS Mathematics
Unit: 06 Lesson: 01
Squaring and Rooting: Inverses
Warm-Up
Solve each equation for x. Remember: These equations usually have two solutions.
A) x 2  21  70
B) 4 x 2  12  13
1. Review of Quadratic Functions
A. For the equation y = x 2 , complete
the table. Then plot points to
construct the graph.
B. If the domain of the equation is
3, 2, 1,0,1,2,3 , then what
would be the range?
C) ( x  3)2  4  40
y = x2
x
y
-3
-2
4
-1
0
-4
4
1
2
C. Is this equation a function?
Explain.
-4
3
2. Inverse with Coordinates
A. Recall that an inverse can be
formed by switching the x- and ycoordinates in a relation. Use this
method to make a table and graph
for the inverse of y = x 2 .
Inverse
x
y
-3
-2
4
-1
B. Is this inverse a function?
Explain.
0
1
-4
4
2
3
3. Inverse with Algebra
Remember that another way
to find an inverse is to switch
the x and y variables in an
equation, then solve for the
“new” y.
A. Use this algebraic method
to find the inverse of
y = x2 .
©2012, TESCCC
Equation:
Inverse:
y = x2
____ = ____2
-4
B. Use a calculator to help you sketch
the graph of this inverse equation
in the box below.
Solve:
Notation: f - 1( x ) =
Does this graph match your answer
from #2? Explain.
Editable Resource Document (ERD)–Content may be modified (DULA terms and conditions still apply)
Algebra 2
HS Mathematics
Unit: 06 Lesson: 01
Squaring and Rooting: Inverses
These two relations are inverses of one another.
Graph:
What are the properties of
inverses?
y

Graph:
y
Their graphs are
_________________ over the
x
x
line ___________
Equation:

Their equations have the
Equation:
_______________ switched
Shape:
Shape:
What’s the “PROBLEM” with this graph?
This graph is ___________ a ________________!
So, normally…
We just graph the _______ ___________ and call it the _____________ _____________ function.
Graph:
Domain:
Parent function:
f (x) = x
Table:
x
0
1
4
9
__________________
(You can only use ____________
y
0
1
2
3
values for _____.)
2
Range:
2
4
6
8
__________________
(You will only get ____________
answers for _____.)
©2012, TESCCC
Editable Resource Document (ERD)–Content may be modified (DULA terms and conditions still apply)
Algebra 2
HS Mathematics
Unit: 06 Lesson: 01
Squaring and Rooting: Inverses
4. Review of Quadratic Transformations
x
y  2x 2  2
-2
A. For the equation above,
-1
complete the table. Then plot
0
points to construct the graph.
1
2
y
4
-4
4
B. This graph is a transformation of the parent graph
y = x 2 . Tell how each constant in the equation
changes the graph of the parent function.

What affect does the “−2” have on the graph?

What affect does the “2” coefficient have on the
graph?
5. Inverse with Coordinates
A. Again, recall that an inverse
can be formed by switching
the x- and y- coordinates in a
relation. Use this method to
make a table and graph for
the inverse of y  2x 2  2 .
x
-4
y
-2
-1
0
1
2
B. Is this inverse a function? Explain.
4
-4
4
-4
6. Inverse with Algebra
Remember that another way
to find an inverse is to switch
the x and y variables in an
equation, then solve for the
“new” y.
Equation:
Inverse:
y  2x 2  2
B. Use a calculator to help you
sketch the graph of this
inverse equation in the box
below.
Solve:
A. Use this algebraic method
to find the inverse of
y  2x 2  2 .
Notation:
©2012, TESCCC
Does this graph match your
answer from #5? Explain.
Editable Resource Document (ERD)–Content may be modified (DULA terms and conditions still apply)
Algebra 2
HS Mathematics
Unit: 06 Lesson: 01
Squaring and Rooting: Inverses
7. Review of Quadratic Transformations
y  ( x  3)2  1
x
0
A. For the equation above,
complete the table. Then plot
points to construct the graph.
y
1
2
4
3
B. This graph is a transformation of
the parent graph y = x 2 . Tell
how each constant in the
equation changes the graph of
the parent function.
4
-4
6
-4

What affect does the “−3” have on the graph?

What affect does the “−1” have on the graph?
8. Inverse with Coordinates
A. Again, recall that an inverse
can be formed by switching
the x- and y- coordinates in a
relation. Use this method to
make a table and graph for
the inverse of y  ( x  3)2  1 .
4
5
x
y
0
1
2
4
3
4
B. Is this inverse a function?
Explain.
-4
4
5
6
-4
9. Inverse with Algebra
Remember that another way
to find an inverse is to switch
the x and y variables in an
equation, then solve for the
“new” y.
Equation:
Inverse:
y  ( x  3)2  1
B. Use a calculator to help you
sketch the graph of this
inverse equation in the box
below.
Solve:
A. Use this algebraic method
to find the inverse of
y  ( x  3)2  1 .
Notation:
©2012, TESCCC
Does this graph match your
answer from #8? Explain.
Editable Resource Document (ERD)–Content may be modified (DULA terms and conditions still apply)
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Squaring and Rooting Inverses