Free Printable Quadratic Inequalities

1.

Solve the inequality:

g\left(x\right)<0

a)

$\left(-1,4\right)$

b)

$\left(-\infty,-1\right)\cup\left(4,\infty\right)$

c)

$\left(-\infty,0\right)\cup\left(0,\infty\right)$

d)

$\left(-\infty,-1\right]\cup\left[4,\infty\right)$

2.

Solve the inequality:

g\left(x\right)\ge0

Type your answer in interval notation. Don't insert spaces between characters.

(a)

3.

Solve $g\left(x\right)\ge f\left(x\right)$

a)

$\left(-\infty,-2\right)\cup\left(1,\infty\right)$

b)

$\left(-\infty,-2\right]\cup\left[1,\infty\right)$

c)

$\left(-2,1\right)$

d)

$\left[-2,1\right]$

4.

Solve $f\left(x\right)>g\left(x\right)$

a)

$\left(-\infty,-2\right)\cup\left(1,\infty\right)$

b)

$\left(-\infty,-2\right]\cup\left[1,\infty\right)$

c)

$\left(-2,1\right)$

d)

$\left[-2,1\right]$

5.

Given the function

f\left(x\right)\ =\ x^2-3x-10

, find the x-intercepts. Check all that apply.

Note: The next few problems will use this function. You may want to record your answers.

a)

-5

b)

5

c)

2

d)

-2

6.

Given the function

f\left(x\right)=\ x^2-3x-10

, find the y-intercept. Enter your answer as an ordered pair.

(a)

7.

Given the function

f\left(x\right)=\ x^2-3x-10

, does the graph open up or down?

a)

Up

b)

Down

8.

Given the function

f\left(x\right)=\ x^2-3x-10

, find the vertex.

a)

(1.5, 12.25)

b)

(-1.5, -3.25)

c)

(1.5, -12.25)

d)

(1.5, 3.25)

9.

Given the function

f\left(x\right)=\ x^2-3x-10

, what is the axis of symmetry?

a)

x = 1.5

b)

x = -1.5

c)

y = 1.5

d)

y = -12.25

10.

Given the function

f\left(x\right)=\ x^2-3x-10

, find

f\left(x\right)>0

.

a)

$\left(-\infty,-2\right)\cup\left(5,\infty\right)$

b)

$\left(-2,5\right)$

c)

$\left(-\infty,-2\right]\cup\left[5,\infty\right)$

d)

$\left[-2,5\right]$

11.

Given the function

f\left(x\right)=\ x^2-3x-10

, find

f\left(x\right)\le0

.

a)

$\left(-\infty,-2\right)\cup\left(5,\infty\right)$

b)

$\left(-2,5\right)$

c)

$\left(-\infty,-2\right]\cup\left[5,\infty\right)$

d)

$\left[-2,5\right]$

12.

A ball is thrown vertically upward with an initial velocity of 96 feet per second. The distance s (in feet) of the ball from the ground after t seconds is:
$s\left(t\right)=96t-16t^2$

At what time t will the ball strike the ground? Hint: Find the x-intercepts.

a)

0 seconds

b)

3 seconds

c)

6 seconds

d)

12 seconds

13.

A ball is thrown vertically upward with an initial velocity of 96 feet per second. The distance s (in feet) of the ball from the ground after t seconds is:
$s\left(t\right)=96t-16t^2$

For what time t is the ball more than 128 feet above the ground?

Hint: Solve $s\left(t\right)>128$ .

a)

From 0 to 2 seconds

b)

From 1 to 3 seconds

c)

From 2 to 4 seconds

d)

From 3 to 5 seconds

Quadratic Inequalities

Total questions: 13

Worksheet time: 34mins

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