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Worksheets

Quadratic Equations/Complete Square Test

Total questions: 80

Worksheet time: 5hrs 40mins

Name
Class
Date
1.

Solve

x2 + 2x - 20 = 4

a)

x = -6, x = 4

b)

x = 6, x = -4

c)

x = 12, x = -2

d)

x = 8, x = -3

2.
Solve
x2 + 9x + 20 = 0
a)
x = -2, x = -10
b)
x = -3, x = -4
c)
x = -4, x = -5
d)
x = -4, x = -6
3.

Solve

(n +7)(n + 9) = 0

a)

n = -7; n = 4

b)

n = 7; n = -9

c)

n = -3; n = 10

d)

n = -7; n = -9

4.
What property would you use to solve the following?
(x-3)(x+2)=0
a)
Commutative Property
b)
Associative Property
c)
Zero Product Property
d)
Inverse Property
5.
What should you do first in solving this equation?
x2 + 6x - 13 = 3
a)
Get factored form
b)
Find two numbers which add to make 6 and multiply to make -13
c)
Make it equal 0 by subtracting 3 on each side
d)
Type it all in a calculator.
6.

Solve the equation using the zero product property.

3x(2x - 4) = 0

a)

x = -1/3 or x = -2

b)

x = 0 or x = 2

c)

x = 0 or x = -2

d)

x = -1/3 or x = 2

7.
Factor x2 + 6x + 9 and solve for x. 
a)
(x+3)(x+3); x = -3
b)
(x+4)(x+5); x=-4, -5
c)
(x-3)(x-3); x=3
d)
Not factorable
8.

Solve using Zero-Product Property.

(2x - 2)(5x + 5) = 0

a)

x = -1

b)

x = -1 or x = 1

c)

x = 1

d)

x = -2 or x = 5

9.
If the graph of a quadratic does not intercept the x-axis at any point, then it has:
a)
1 Real Solution
b)
2 Real Solutions
c)
Half a Solution
d)
No Real Solution
10.

Solve by factoring

x2+12x+35=0

a)

x = -5 or x = -7

b)

x = 5 or x = 7

c)

x = -35 or x = -1

d)

x = -9 or x = -4

11.
Solve by factoring:
x2 + 2x - 24 = 0
a)
x = -6, x = 4
b)
x = 6, x = -4
c)
x = 12, x = -2
d)
x = 8, x = -3
12.

Solve by factoring:

x2 + 6x + 20 = -3x

a)

x = -2, x = -10

b)

x = -3, x = -4

c)

x = -4, x = -5

d)

x = -4, x = -6

13.

Solve by Factoring

x2 + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

14.
What are the solutions to this equation? (x-3)(x+2)=0
a)
x=3,-2
b)
x=-3,2
c)
x=2,3
d)
x=3,2
15.
Solve by factoring:
x2 - 6x + 5 = 0
a)
-6, -1
b)
-5, -1 
c)
1, 6
d)
5, 1
16.
Solve
16a2 - 9 = 0
a)
a = -3/4, 3/4 
b)
a = -4/3, 4/3 
c)
a = -9/16, 9/16 
d)
a = -16/9, 16/9 
17.
Solve
a2 + 2a - 24 = 0
a)
a = -6, 4
b)
a = 6, -4
c)
a = 12, -2
d)
a = 8, -3
18.
Solve
8n2 + 10n - 3 = 0
a)
n = -1/8, 10/3
b)
n = 4/5, - 2
c)
n = 1/4, -3/2
d)
n = 2, -12
19.
Solve using Zero-Product Property.
(2x-2)(5x-5) = 0
a)
x = -1
b)
x = -1 or x = 1
c)
x = 1
20.
Solve:
x2 - 49 = 0
a)
x = -7, x = 7
b)
x = -7
c)
x = 7
d)
x = -7, x = 1
21.
n² - 2n = 0
a)
n = 2 and 0
b)
n = -2 and 0
c)
n = 2
d)
n = 0
22.

What are the zeros of the function below?

f(x)=(x - 6)(2x + 4)

a)

x = -6, x = -4

b)

x = 6, x = -2

c)

x = 4, x = 6, x =2

d)

cannot be determined

23.
Solve by factoring.
z2 - 18z + 81 = 0
a)
z = 9
b)
z = -9
c)
z = 9 or z = -9
24.
a)
±1.5
b)
1.5
c)
±1
d)
No real solution
25.

What is the standard form formula?

a)

y=mx+b

b)

y=ax2+bx+c

c)

y=a(x-h)2+k

26.

What is the vertex form formula?

a)

y=ax2+bx+c

b)

y=mx+b

c)

y=a(x-h)2+k

27.

Is the graph shown above a max or min?

a)

Maximum

b)

Minimum

28.

What is the domain of the graph shown above.

a)

x=19

b)

all real numbers

c)

y=3

d)

Maximum

29.

What are the zeros of the graph shown above?

a)

2 and 6

b)

4 and 2

c)

6 and 9

d)

5 and 1

30.

What is a axis of symmetry?

a)

all real numbers

b)

y=5

c)

the line that divides the graph in equal halves

d)

y=mx+b

31.

Is the graph shown above a max or min?

a)

Minimum

b)

Maximum

32.

What is the y-intercept of the graph shown above?

a)

all real numbers

b)

(0,6)

c)

(0,2)

d)

(0,-6)

33.

What is the vertex of the graph shown above?

a)

(7,6)

b)

(-1,2)

c)

(2,-1)

d)

(5,0)

34.

Graph the following equation:

y=x2-2x-3

a)
b)
c)
d)
35.

Which value is the vertex?

a)

(-4, 0)

b)

(-1, -9)

c)

(0, -8)

d)

(2, 0)

36.

Does this graph have a maximum or a minimum?

a)

maximum

b)

minimum

c)

I am not sure.

d)

neither

37.

Does this graph have a maximum or a minimum?

a)

maximum

b)

minimum

c)

I am not sure.

d)

neither

38.

Does the equation open or or down? Is the vertex a maximum or minimum?

Y = -3x2 +7x - 2

a)

up, minimum

b)

down, maximum

c)

up, maximum

d)

down, minimum

39.

True or false:

The solution, root, x-intercept, and zero are all the same thing.

a)

True

b)

False, because the solution and root are the same but the x-intercept and zero are different

c)

False, because the x-intercept and root are the same but the zero and solution are different

d)

False, they are all different

40.

What are the zeroes of this graph?

a)

x = -4 and 2

b)

x= -1 and 0

c)

x = 9 and -8

d)

x= 4 and -2

41.
When factoring
x2 - 4x + 4 = 20,
what goes in the blank?
(x - __ )2 = 20
a)
4
b)
2
c)
8
d)
20
42.
Complete the square.
x2 + 6x + ____
a)
x2 + 6x + 9
b)
x2 + 6x - 36
c)
x2 + 6x + 36
d)
x2 + 6x - 9
43.
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
44.
Complete the square for
x2 + 12x + ____
a)
x2 + 12x + 144
b)
x2 + 12x + 36
c)
x2 + 12x - 36
d)
x2 + +12x - 144
45.
Complete the square.
x2 + 14x + ____
a)
x2 + 14x - 196
b)
x2 + 14x + 49
c)
x2 + 14x - 49
d)
x2 + 14x + 196
46.
Complete the Square
x2 + 10x + ____
a)
x2 + 10x - 100
b)
x2 + 10x + 100
c)
x2 + 10x - 25
d)
x2 + 10x + 25
47.
What is one of the solutions to this equation?
(2x - 1)2 = 49
a)
7
b)
-7
c)
-4
d)
-3
48.
Solve the equation by completing the square and then finding the roots. 
x2+ 6x - 4 = 36
a)
x = -7, 7
b)
x = 4, -10
c)
x = -4 +- √7
d)
x = 10, -4
49.
Solve the following equation by completing the square:
n2 - 2n - 3 = 0
a)
{3 and-1}
b)
{4 and -4}
c)
{5 and -3}
d)
{8 and -7}
50.
Solve by completing the square.
y2 + 10y = -9
a)
1 and -12
b)
-1 and -9
c)
1 and -9
d)
1 and -1
51.
Solve by completing the square.
x2 +12x = 5
a)
X = 6 + √41 or  6 − √41
b)
X= 35 or 47
c)
X = −6 + √41 or  −6 − √41
d)
X = √35 or √47
52.
Solve by completing the square:
k2 − 12k + 23 = 0
a)
{6 + √13, 6 - √13}
b)
{-6 + √13, -6 - √13}
c)
{6 + √59, 6 - √59}
d)
{-6 + √59, -6 - √59}
53.
a)
A
b)
B
c)
C
d)
D
54.
Solve
 3x² + 5x - 12 = 0
a)
x = -4/3, x = 3
b)
x = 4/3, x = -3
c)
x = -1, x = 4
d)
x = 1, x = -4
55.

Find the value of "c" that completes the square.

x2+8x+cx_{ }^2+8x+c  

a)

-4

b)

4

c)

8

d)

16

56.

Find the value of "c" that completes the square.

x2+28x+cx^2+28x+c  

a)

28

b)

14

c)

196

d)

56

57.
What do you do to the b value to correctly complete the square?
a)
square it
b)
divide it by 2 and square the result
c)
divide it by 2 and take the square root of the result
d)
divide it by 2 only
58.
To solve by completing the square, what needs to be moved in this equation?
x2 = 9 - 4x
a)
the -4x
b)
the 9
c)
the x2
59.
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
60.
When factoring
x2 - 4x + 4 = 20,
what goes in the blank?
(x - __ )2 = 20
a)
4
b)
2
c)
8
d)
20
61.
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
62.

x2+12x+x^2+12x+  ___

Complete the square!

a)

x2 + 12x + 144

b)

x2 + 12x + 36

c)

x2 + 12x - 36

d)

x2 + 12x - 144

63.

Complete the square.

x2 - 14x + ____

a)

- 196

b)

49

c)

- 49

d)

28

64.
Which of the following equations matches standard form of a quadratic?
a)
ax + by = c
b)
y = a(x - h)2 + k
c)
y = ax2 + bx + c
d)
y = mx + b
65.

What is the vertex of the equation

y=(x−3)2+5y=\left(x-3\right)^2+5  

a)

(-3, 5)

b)

(3, 5)

c)

(-3, -5)

d)

(3, -5)

66.

What is the vertex of the equation

y=(x+7)2+3y=\left(x+7\right)^2+3  

a)

(7, 3)

b)

(7, -3)

c)

(-7, 3)

d)

(-7, -3)

67.
When do you use the plus or minus symbol?
±
a)
After taking the square root of both sides
b)
After adding the square to both sides
c)
After taking half of b
d)
After setting the equation equal to zero
68.
When do you use the plus or minus symbol?
±
a)
After taking the square root of both sides
b)
After adding the square to both sides
c)
After taking half of b
d)
After setting the equation equal to zero
69.
When do you use the plus or minus symbol?
±
a)
After taking the square root of both sides
b)
After adding the square to both sides
c)
After taking half of b
d)
After setting the equation equal to zero
70.

Convert to vertex form:


y = x2 + 14x + 50

a)

y = (x + 7)2 + 1

b)

y = (x - 7)2 - 1

c)

y = (x + 7)2 - 50

d)

y = (x + 7)2 - 1

71.

Convert to vertex form:


y = x2 + 20x + 88

a)

y = (x + 10)2 + 12

b)

y = (x - 10)2 - 12

c)

y = (x - 10)2 + 12

d)

y = (x + 10)2 - 12

72.

Convert to vertex form:


y = x2 - 14x + 36

a)

y = (x + 7)2 + 13

b)

y = (x - 7)2 - 13

c)

y = (x - 7)2 + 13

d)

y = (x + 7)2 - 13

73.

Complete the square

2x2−20x+18=02x^2-20x+18=0  

a)

x={1,9}x=\left\{1,9\right\}  

b)

x={−1,−9}x=\left\{-1,-9\right\}  

c)

x={1,18}x=\left\{1,18\right\}  

d)

x={5,9}x=\left\{5,9\right\}  

74.

Complete the square

3x2+15=18x3x^2+15=18x  

a)

x={−1,5}x=\left\{-1,5\right\}  

b)

x={2,25}x=\left\{2,25\right\}  

c)

x={1,5}x=\left\{1,5\right\}  

d)

x={5,20}x=\left\{5,20\right\}  

75.
Create a Perfect Square Trinomial
x2 + 6x + ____
a)
6
b)
-6
c)
9
d)
-9
76.
Create a Perfect Square Trinomial
x2 + 22x + ____
a)
11
b)
- 11
c)
121
d)
-121
77.
Create a Perfect Square Trinomial
x2 + 18x + ____
a)
81
b)
-18
c)
9
d)
-9
78.
Create a Perfect Square Trinomial
x2 - 30x +  ____
a)
-15
b)
225
c)
30
d)
25
79.
Create a Perfect Square Trinomial
x2 - 4x +  ____
a)
2
b)
-2
c)
4
d)
16
80.
Create a Perfect Square Trinomial
x2 - 2x +  ____
a)
2
b)
4
c)
-2
d)
1

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