Free Printable Algebra 1: Topic 9 (Solving Quadratic Equations)

1.

Solve by factoring: x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

2.

Solve by factoring: x² + 3x - 18 = 0

a)

x = -3 and x = 6

b)

x = 3 and x = -6

c)

x = -9 and x = 2

d)

x = 9 and x = -2

3.

Solve by taking square roots:

5b² - 4 = 41

a)

b = 9, b = -9

b)

b = 3, b = -3

c)

b = 8, b = -8

d)

no real solution

4.

Solve for x:

(x + 6)²= 49

a)

x=7,12

b)

x=±7

c)

x=1,-13

d)

x=43,-55

5.

What should you do first to solve this equation using 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.

6.

In the equation

x² - 5x + 7= 0,

match each leading coefficient with its correct letter

for a, b and c

a)

a = 0, b = 5, c = 7

b)

a = 1, b = -5, c = 7

c)

a = 7, b = 5, c = 1

d)

a = 1, b = 5, c = 7

7.

Solve: 2(x - 3)² - 14 = 18

a)

1, 7

b)

-1, 7

c)

-1, -7

d)

1, -7

8.

k² - 2k = 0

a)

k = 2 and 0

b)

k = -2 and 0

c)

k = 2

d)

k = 0

9.

Simplify:

a)

81√3

b)

9√3

c)

3√3

d)

√3

10.

Simplify the radical - 6√90

a)

10√8

b)

10√18

c)

18√10

d)

18√9

11.

Simplify:

a)

2√3√14

b)

4√42

c)

2√42

d)

4√3√14

12.

Simplify:

a)

4√30

b)

√4√30

c)

√2√30

d)

2√30

13.

a)

A

b)

B

c)

C

d)

D

14.

a)

A

b)

B

c)

C

d)

D

15.

a)

A

b)

B

c)

C

d)

D

16.

Solve by completing the square.
x² + 4x= 12

a)

x = 2 and -2

b)

x = -6 and 2

c)

x = 6 and -2

d)

x = 1 and -1

17.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

18.

Solve using the Quadratic Formula:

2x² + 2x − 12 = 0

a)

x = −2, 3

b)

x = 2, 3

c)

x = 2, −3

d)

x = −2, −3

19.

Solve by factoring. (HINT: Factor GCF 1st)

a)

x = 3, x = -6

b)

x = 0, x = 2

c)

x = 2, x = 3

d)

x = -2, x = 1

20.

What number added would make a perfect square trinomial?

x² - 8x + ______

a)

-4

b)

-64

c)

12

d)

16

21.

Factor Completely:
3x² + 18x +15

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

22.

Which is the standard form for a quadratic equation?

a)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

b)

$ax^2+bx+c=0$

c)

$y=a\left(x-h\right)^2+k$

d)

$a^2+b^2=c^2$

23.

Given this graph is the function of

y=x^2-2x-8

, what is the solution to

x^2=2x+8

?

a)

(1, 9)

b)

x = {-2, 4}

c)

(0, 8)

d)

x = {5, 2}

24.

$3x^2-10x+1=0$

Solve by the method of your choice.

a)

$x=\frac{-10\pm\sqrt{88}}{6}$

b)

$x=\frac{-5\pm2\sqrt{22}}{3}$

c)

$x=\frac{10\pm\sqrt{112}}{6}$

d)

$x=\frac{5\pm\sqrt{22}}{3}$

25.

$2x^2=8x+3$

2x^2-8x-3=0

x=\frac{8\pm\sqrt{64-4\left(2\right)\left(-3\right)}}{4}

x=\frac{8\pm\sqrt{40}}{4}

x=\frac{8\pm2\sqrt{10}}{4}

x=\frac{4\pm\sqrt{10}}{2}

Suzanne solved the equation using this process.

Did she make a mistake?

If yes, at which line did she make her first mistake?

(There are 5 steps in her process)

a)

Suzanne made no errors.

b)

Step 2

c)

Step 3

d)

Step 4

e)

Step 5

26.

What is the color of the graph that has exactly one real zero?

a)

black

b)

green

c)

purple

d)

red

e)

None of these graphs has exactly one zero.

27.

How many real solutions can a quadratic equation of the form shown have?
Check all that apply.

ax^2+bx+c=0

a)

0

b)

1

c)

2

d)

3

e)

infinitely many

28.

What are the zeros?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

29.

What is another word for zeros?

a)

y-intercepts

b)

roots

c)

vertex

d)

axis of symmetry

30.

How many zeros does this parabola have?

a)

3

b)

2

c)

0

d)

1

31.

Find the zeros of the quadratic equation y=4(x+9)²-36

a)

x=-9+√6 & x=-9-√6

b)

x=3 & x=-3

c)

x=-6 & x=-12

d)

so solution

32.

What is the first step to solving THIS equation by completing the square?
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

33.

Complete the Square

x² + 6x - 5

a)

(x + 3)² = 5

b)

(x + 6)² = 9

c)

(x + 3)² = 14

d)

(x + 6)² = 14

34.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

35.

Solve $\left(x+3\right)^2-13=0$ , leave your answer in the form of $p\pm\sqrt[]{q}$

a)

$x=-3\pm\sqrt[]{13}$

b)

$x=3\pm\sqrt[]{13}$

c)

$x=-3\pm\sqrt[]{-13}$

d)

$x=-3-\sqrt[]{13}$

36.

Solve $\left(x+5\right)^2-20=0$ , and leave your answer in the form $p\pm\sqrt[]{q}$

a)

$x=-5\pm\sqrt[]{20}$

b)

$x=5\pm\sqrt[]{20}$

c)

$x=5+\sqrt[]{20}$

d)

$x=-5-\sqrt[]{20}$

37.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

38.

Complete the Square
x² + 6x = 5

a)

(x + 3)² = 5

b)

(x + 6)² = 9

c)

(x + 3)² = 14

d)

(x + 6)² = 14

39.

Solve the equation:
5x² - 35x + 60 = 0

a)

x = 3, -4

b)

x = -3, 4

c)

x = 3, 4

d)

x = -3, -4

40.

Solve by completing the square.
y² + 10y = -9

a)

1 and -12

b)

-1 and -9

c)

1 and -9

d)

1 and -1

41.

What is this formula?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

42.

In the equation
y = x² +5x +7, match each leading coefficient with its correct letter

a)

a=0, b=5, c=7

b)

a=1, b=5, c=7

c)

a=7, b=5, c=1

43.

What should you do first in solving this equation?
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.

44.

Solve Using the Quadratic Formula
2x² + 7x - 15 = 0

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

45.

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

46.

Solve by the Quadratic Formula:

$-12q^2+3q+7=0$

a)

$\frac{-3\pm\sqrt{345}}{24}$

b)

$\frac{3\pm\sqrt{345}}{-24}$

c)

$\frac{3\pm\sqrt{345}}{24}$

d)

$\frac{3\pm i\sqrt{39}}{24}$

47.

If b²-4ac is positive, the quadratic equation has:

a)

Two real solutions that are different

b)

Two imaginary solutions that are different

c)

One real solution

d)

One imaginary solution

48.

If b²-4ac is negative, the quadratic equation has:

a)

Two real solutions that are different

b)

Two imaginary solutions that are different

c)

One real solution

d)

One imaginary solution

49.

If b²-4ac is 0, the quadratic equation has:

a)

Two real solutions that are different

b)

Two imaginary solutions that are different

c)

One real solution

d)

One imaginary solution

50.

The height of an item falling can be modeled by h_t = -16t² + h_o . Where h_o is the initial height in feet, and h_t is the height in feet at time t in seconds. If I drop a penny at a height of 18.6 feet, how long will it take the item to hit the ground?

a)

1.08 seconds

b)

2.08 seconds

c)

0.08 seconds

d)

1.17 seconds

51.

The height of an item falling can be modeled by h_t = -16t² + h_o . Where h_o is the initial height in feet, and h_t is the height in feet at time t in seconds. If I drop a cup at a height of 18.9 feet, how long will it take the item to hit the ground?

a)

2.09 seconds

b)

1.09 seconds

c)

1.19 seconds

d)

0.09 seconds

52.

You and some friends went to a haunted house on Halloween. The mummy scared one friend so much that she jumped into the air! The equation h = -4t² + 2t models her jump where h is her jump's height in feet t seconds after the mummy scares her. When did she reach her maximum height?

a)

0.1 seconds

b)

0.25 seconds

c)

0.50 seconds

d)

1 second

e)

2 seconds

53.

A frog is sitting on the ground when he is scared by a big dog. His movement is modeled by the equation h = -6t²+ 6t where h is the frog's height at any given time, t . How many seconds until the frog is back on the ground?

a)

0.5 seconds

b)

1 second

c)

1.5 seconds

d)

2 seconds

e)

3 seconds

Algebra 1: Topic 9 (Solving Quadratic Equations)

Total questions: 53

Worksheet time: 2hrs 28mins

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