Free Printable Inequalities Quadratics

1.

Match the graph to its inequality.

a)

$y>-x^2-5x-6$

b)

$y>x^2+x-6$

c)

$y<x^2-5x+6$

d)

$y<-x^2-x+6$

2.

Which of the following is not a solution to this system of inequalities?

a)

(0,-1)

b)

(0,3)

c)

(4,0)

d)

(6,-2)

3.

Solve using the quadratic formula

x² + 6x = -8

a)

x= 1.125, -7.125

b)

x= 4, 2

c)

x= -1.125, 7.125

d)

x= -4, -2

4.

Solve this inequality:

5x - 3 ≤ 27

a)

x ≤ 4 ⅘

b)

x ≥ 6

c)

x ≤ 6

d)

x ≥ 4 ⅘

5.

Which of the following is the solution of the given Quadratic Inequality?

a)

5 < y < 12

b)

7 < y < 10

c)

8 < y < 9

d)

6 < y < 11

6.

3x - x²> 0

a)

(−∞, 0) U (3, ∞)

b)

(−∞, - 3) U (0, ∞)

c)

(-3, 0)

d)

(0, 3)

7.

Which inequality is shown?

a)

y< -x²

b)

y≤ -x²

c)

y> -x²

d)

y≥ -x²

8.

Which of the following is the solution of the given Quadratic Inequality?

a)

b ≥ -2 or b ≤ -1

b)

b ≤ -2 or b ≥ -1

c)

b ≥ 2 or b ≤ 1

d)

b ≤ 2 or b ≥ 1

9.

Which inequality is represented by the graph?

a)

y > (x - 3)² - 3

b)

y ≥ (x + 3)² - 3

c)

y > (x + 3)² - 3

d)

y ≥ (x - 3)² - 3

10.

-4x -7 ≥ 21

a)

x ≤ -7

b)

x ≥ -7

c)

x ≤ 8

d)

x ≤ -8

11.

Solve the inequality: 7y - 4 ≤ 3y + 8

a)

y < -2

b)

y = 0

c)

y ≤ 4

d)

y ≥ 12

12.

Solve for x
2x−32<15

a)

47

b)

23.7

c)

23.5

d)

4

13.

3x − (2 + 6x) ≤ -32

a)

x ≥ 10

b)

x< -10

c)

x ≥ -10

d)

All real numbers

14.

-3 − 6(4x + 6) > -111

a)

x > 3

b)

x < 3

c)

x < -3

d)

x > -3

15.

a)

y ≥ -x² - 8x -15

b)

y < -x²+ 8x - 15

c)

y ≤ x² - 8x + 17

d)

y ≤ -x² + 8x - 15

16.

Which of the following graphs represents the solution to the inequality $y < -x^2 + 2x + 1$ ?

a)

A parabola opening upwards with the region above the curve shaded.

b)

A parabola opening upwards with the region below the curve shaded.

c)

A parabola opening downwards with the region above the curve shaded.

d)

A parabola opening downwards with the region below the curve shaded.

17.

A quilting group is adding a border to aquilt top using their existing fabric stash. They have at most 3600 square inches of fabric to use for the quilt border. The function $b\left(x\right)=4x^2+364x$ represents the area of the quilts border, where x is the width of the border in inches. Solve the inequality $4x^2+364x\le3600$ to determine what border widths the quilters may choose.

4 lines

18.

What is the solution set for
-5x + 12 > -28

a)

x > 8

b)

x < 8

c)

x > -8

d)

x < -8

19.

Which inequality is represented by the graph?

a)

y > -(x - 4)² + 1

b)

y > -(x - 1)² + 4

c)

y < (x - 4)² + 1

d)

y > (x + 4)² + 1

20.

Solve equation by using the quadratic formula $9x^2+24x=-16$

a)

$x=-\frac{4}{3}$

b)

$x=\frac{4}{3}$

c)

$x=\frac{3}{4}$

d)

$x=-\frac{3}{4}$

Inequalities Quadratics

Total questions: 20

Worksheet time: 20mins

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