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3.06 Quadratic inequalities

Adaptive
Worksheet

Interactive practice questions

Consider the inequality $x^2-3x-10\ge0$x23x100.

a

First factor $x^2-3x-10$x23x10.

b

For what values of $x$x is $x^2-3x-10=0$x23x10=0? Leave your solutions on the same line separated by a comma.

c

To solve the inequality, Micky splits up the entire number line into three intervals, and tests a value from each interval to see if it satisfies the inequality $x^2-3x-10\ge0$x23x100.

Interval A ($x<-2$x<2) $x=-2$x=2

Interval B ($-22<x$<$<$5$5)

$x=5$x=5 Interval C ($x>5$x>5)
Value to test   Value to test   Value to test
$x=-3$x=3   $x=1$x=1   $x=7$x=7

Which values of $x$x satisfy the inequality $x^2-3x-10\ge0$x23x100? Select all that apply.

$x=7$x=7

A

$x=-3$x=3

B

$x=1$x=1

C
d

Hence, state the solution to the inequality $x^2-3x-10\ge0$x23x100. You may use the keywords "and"/"or".

Easy
4min

Consider the inequality $x^2-9\le0$x290.

Easy
1min

Consider the inequality $x^2-x-20<0$x2x20<0.

Medium
1min

Consider the inequality $-x^2+x+20\le0$x2+x+200.

Medium
2min
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Outcomes

M2.A.CED.A.1

Create equations and inequalities in one variable and use them to solve problems in a real-world context.*

M2.A.REI.B.2

Solve quadratic equations and inequalities in one variable.

M2.A.REI.B.2.B

Solve quadratic inequalities using the graph of the related quadratic equation.

M2.MP1

Make sense of problems and persevere in solving them.

M2.MP3

Construct viable arguments and critique the reasoning of others.

M2.MP6

Attend to precision.

M2.MP7

Look for and make use of structure.

M2.MP8

Look for and express regularity in repeated reasoning.

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