IXL - Find the inverse of a quadratic function (Algebra 2 practice)

Find the inverse of the function.

(

–

)

Write your answer in the form

where

and

are constants. Simplify any fractions.

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Learn with an example

question

Find the inverse of the function.

(

–

)

Write your answer in the form

where

and

are constants. Simplify any fractions.

key idea

A relation is a set of ordered pairs

(

)

If a relation pairs each

-value

with exactly one

-value,

the relation is called a

function.

The inverse of a relation has the

and

-values

swapped. So, if

(

)

is an ordered pair of the relation, then

(

)

is an ordered pair of its inverse. If the inverse of a function is also a

function,

then it is called the inverse

function.

When it's not specified, the domain of a relation is the set of all possible

-values.

Sometimes a smaller domain will be specified.

solution

To find the inverse of the function

(

–

)

Swap the
x
and
y
variables.
Solve for the new
y
variable.

Swap the

and

variables.

(

–

)

(

–

)

Solve for the new

variable.

First isolate the quantity that is squared. Then take the square root and solve for

(

–

)

Take the square root of both sides

–

Take the square root of both sides

So, the inverse is

This is not a function because there are input values which have two output values. For example, if

then

In other words,

(

)

and

(

)

are both points in the inverse relation (corresponding to the points

(

)

and

(

)

in the original function).

Looking for more? Try these:

Lesson: Inverse functions

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Not feeling ready yet? These can help:

CC.3Find the inverse of a linear function

Z.1Solve a quadratic equation using square roots

Lesson: Inverse functions

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