Free Printable Quadratic Equations Unit Review

1.

Solve. $3x^2+2x-1=0$

a)

$x=\frac{1}{3}\ or\ x=-1$

b)

$x=-\frac{1}{3}\ or\ x=1$

c)

$x=-1\ or\ x=3$

d)

$x=1\ or\ x=-3$

2.

Solve. $x^2+12x=4$

a)

$6\pm2\sqrt{10}$

b)

$-6\pm2\sqrt{10}$

c)

$-6\pm\sqrt{40}$

d)

$6\pm\sqrt{40}$

3.

Solve. $x^2+7x=-10$

a)

$x=-5\ or\ x=2$

b)

$x=5\ or\ x=-2$

c)

$x=-5\ or\ x=-2$

d)

$x=5\ or\ x=2$

4.

Solve. $2x^2-9x-5=0$

a)

$x=-\frac{1}{2}or\ x=5$

b)

$x=5\ or\ x=-1$

c)

$x=-5\ or\ x=\frac{1}{2}$

d)

$x=10\ or\ x=-1$

5.

What is the maximum or minimum value of the quadratic function pictured?

a)

Minimum: (-2,1)

b)

Maximum: (-2,1)

c)

Minimum: (1,-2)

d)

Maximum: (1,-2)

6.

The vertex of the parabola in (𝒙 − 𝟒)² − 𝟓 is

a)

(-4,-5)

b)

(4,-5)

c)

(4,5)

d)

(-4,5)

7.

Find the solution

81x^2-9=0

a)

$x=\pm3$

b)

$x=\pm9$

c)

$x=\pm\frac{1}{3}$

8.

Below is the profit equation for a bike company. What represents the maximum profit?

Profit = −200x² + 92,000x − 8,400,000

a)

vertex x-value

b)

vertex y-value

c)

zero - x-intercept

9.

Below is the profit equation for a bike company. What price should the company sell the bikes at to make a maximum profit?

Profit = −200x² + 92,000x − 8,400,000

a)

$230

b)

$126

c)

$334

10.

What number completes the square of the following expression?
x² - 12x

a)

-36

b)

36

c)

-6

d)

6

11.

What number completes the square of the following expression?
x² + 5x

a)

25/2

b)

25/4

c)

5/2

d)

25

12.

A quadratic equation has zeros located at $-0.5$ and $7$ . Which equation shows this function?

a)

$y=\left(2x\ -\ 1\right)\left(x\ -\ 7\right)$

b)

$y=\left(2x\ +\ 1\right)\left(x\ -\ 7\right)$

c)

$y=\left(x\ +\ 2\right)\left(x\ +\ 7\right)$

d)

$y=\left(x\ -\ 2\right)\left(x\ -\ 7\right)$

13.

What should you do first in solving this equation using the quadratic formula?

x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

14.

Which statement about $f\left(x\right)\ =\ 45x^2\ -\ x\ \ -\ 2$ is true?

a)

The zeros are $\frac{2}{9}$ and $-\ \frac{1}{5}$ because $f\left(x\right)\ =\ \left(9x\ -\ 2\right)\left(5x\ +\ 1\right)$

b)

The zeros are $-\ \frac{2}{9}$ and $-\ \frac{1}{5}$ because $f\left(x\right)\ =\ \left(9x\ +2\right)\left(5x\ +\ 1\right)$

c)

The zeros are $\frac{2}{9}$ and $\frac{1}{5}$ because $f\left(x\right)\ =\ \left(9x\ -\ 2\right)\left(5x\ -1\right)$

d)

The zeros are $-\ \frac{2}{9}$ and $\frac{1}{5}$ because $f\left(x\right)\ =\ \left(9x\ +\ 2\right)\left(5x\ -\ 1\right)$

15.

Algebraically determine the vertex of the function

a)

(4, -2)

b)

(-4, 14)

c)

(2, 0)

d)

(8, 6)

16.

Which is the correct graph of the function:

a)

b)

c)

d)

17.

What is something that is NOT true about this function?

a)

It is wider than y = 6x² + 8

b)

It opens down

c)

It has an axis of symmetry at x = 0

d)

It is translated up 1 unit from y = x²- 3

18.

Which method would be most efficient for solving the equation?

a)

factoring

b)

completing the square

c)

graphing

d)

quadratic formula

19.

What is the maximum or minimum value of the quadratic function pictured?

a)

Minimum: y = 1

b)

Maximum: x = -2

c)

Minimum: x = -2

d)

Maximum: y = 2

20.

What is the first step to solving this equation if you solve by completing the square (Lesson 9.4)?

a² + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Subtract the 21

21.

For the following quadratic equation, what is the value of c ?

5x² + 7x - 11 = 0

a)

5

b)

7

c)

11

d)

-11

22.

For the following quadratic equation, what is the value of a ?

x² - 7x + 2 = 15

a)

0

b)

x²

c)

-7

d)

1

23.

For the following quadratic equation, what is the value of c ?

x² - 7x + 2 = 15

a)

2

b)

15

c)

-13

d)

17

24.

A ball is thrown into the air with an upward velocity of 100 ft/s. Its height, h, after t seconds is given by the function
h = -16t² + 64t + 960.
What is the maximum height?

a)

960 feet

b)

1008 feet

c)

1024 feet

d)

1152 feet

25.

A ball is thrown into the air with an upward velocity of 100 ft/s. Its height, h, after t seconds is given by the function
h = -16t² + 64t + 960.
When did the ball hit the ground?

a)

10 seconds

b)

2 seconds

c)

5 seconds

d)

7 seconds

26.

A dolphin jumps from the water. The equation h = -16t² + 80t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps?

a)

1 foot

b)

5 feet

c)

96 feet

d)

100 feet

27.

A ball is thrown vertically into the air. Its height in feet after t seconds is given by the equation h(t) = –5t² + 20t, and is graphed below. How high will the ball be after 3 seconds?

a)

20 ft

b)

15 ft

c)

5 ft

d)

10 ft

28.

The height of an object thrown into the air can be modeled by the formula h(t) = -16t2 + 70t + 95, where h(t) is in feet after t seconds.
What is the height of the object after 5 seconds?
Hint: $f\left(5\right)=?$

a)

95 feet

b)

45 feet

c)

70 feet

d)

171.56 feet

29.

A ball is thrown into the air with an upward velocity. Its height, h, after t seconds is given by the function below.
$h=-16t^2+64t+960$
How many seconds did it take for the ball to reach its maximum height?

Hint: look at the vertex and remember that x=seconds and y=height.

a)

10 seconds

b)

64 seconds

c)

960 seconds

d)

2 seconds

30.

$h=-16t^2+64t+960.$ A ball is thrown into the air with an upward velocity of 100 ft/s. Its height, h, after t seconds is given by the function

When did the ball hit the ground?
Hint: when the height (h) = 0 OR the x-intercept

a)

10 seconds

b)

2 seconds

c)

5 seconds

d)

7 seconds

31.

Which equation matches the graph?

a)

b)

c)

d)

32.

which of the following show the quadratic formula being used properly?

a)

$\frac{-7\pm\sqrt{\left(7\right)^2-4\left(1\right)\left(-10\right)}}{2\left(1\right)}$

b)

$\frac{7\pm\sqrt{\left(7\right)^2-4\left(1\right)\left(-10\right)}}{2\left(1\right)}$

c)

$\frac{-10\pm\sqrt{\left(-10\right)^2-4\left(1\right)\left(7\right)}}{2\left(1\right)}$

d)

$\frac{10\pm\sqrt{\left(-10\right)^2-4\left(1\right)\left(7\right)}}{2\left(1\right)}$

Quadratic Equations Unit Review

Total questions: 32

Worksheet time: 2hrs 36mins

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