IXL - Graph solutions to quadratic inequalities (Precalculus practice)

Solve for

and graph the solution.

(

)

(

)

≤

Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of a segment, ray, or line to delete it.

ref_doc_title.

Learn with an example

question

Solve for

and graph the solution.

(

–

)

≥

Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of a segment, ray, or line to delete it.

key idea

A polynomial inequality can be written as

(

)

(

)

≥

(

)

(

)

≤

where

(

)

is a polynomial.

The roots of

(

)

separate the

-axis

into intervals. On each interval,

(

)

is either entirely positive or entirely negative.

This diagram is called a sign chart. It shows whether

(

)

is positive or negative on each interval between its roots. (In this example,

(

)

(

–

)

(

–

)

solution

Look at the polynomial inequality:

(

–

)

≥

Since the inequality is not strict (≥), the solution to the inequality is the set of values where the polynomial

(

–

)

is positive or zero.

Create a sign chart.

Start by marking the roots of the polynomial on a number line. You can find the roots by solving

(

–

)

The roots are 0 and 1.

The roots separate the number line into intervals. Find the sign of each factor on each interval.

The factor
x
is negative if
x
<
0
and positive if
x
>
0
.
The factor
x
–
1
is negative if
x
<
1
and positive if
x
>
1
.

Summarize this information in a table. Then, multiply the signs in each column to determine the sign of

(

–

)

on each of the intervals.

	x < 0	0 < x < 1	x > 1
x	-	+	+
x – 1	-	-	+
x ( x – 1 )	+	-	+

The last row of the table shows that

(

–

)

is positive when

negative when

and positive when

Graph the solution.

Graph the intervals where the polynomial is positive or zero. Be sure to include the endpoints of all intervals since the polynomial is zero there.

Looking for more? Try this:

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Teacher tools

Work it out

Not feeling ready yet? These can help:

O.2Solve a quadratic equation using the zero product property

C.1Graph inequalities

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