Free Printable 8.7 Complete The Square

1.

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

2.

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

3.

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

a)

4

b)

2

c)

8

d)

20

4.

What value of c would make this a perfect sqaure trinomial?
x² +8x + c

a)

4

b)

16

c)

64

d)

-16

5.

What value of c would make this a perfect square trinomial?
x² + 2x + c

a)

2

b)

4

c)

-2

d)

1

6.

What value of c would make this a perfect square trinomial?
x²- 12x + c

a)

36

b)

24

c)

144

d)

-36

7.

Complete the Square (this is step before you take square root on both sides)

x² + 6x = 5

a)

(x + 3)² = 5

b)

(x + 6)² = 9

c)

(x + 3)² = 14

d)

(x + 6)² = 14

8.

Find the missing value "c" to create a perfect square trinomial:
x² + 26x + ___

a)

13

b)

136

c)

169

d)

26

9.

Complete the square.
x² + 6x + ____

a)

x² + 6x + 9

b)

x² + 6x - 36

c)

x² + 6x + 36

d)

x² + 6x - 9

10.

$x^2+8x+c=20+c$

Rewrite the above equation into a perfect square binomial form.
(𝑥 +_______) $^2$ = ________

a)

$\left(x-4\right)^2=4$

b)

$\left(x+4\right)^2=36$

c)

$\left(x-8\right)^2=12$

d)

$\left(x+8\right)^2=28$

11.

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

12.

What is one of the solutions to this equation?
(2x - 1)² = 49

a)

7

b)

-7

c)

-4

d)

-3

13.

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

14.

Complete the Square
x² + 10x + ____

a)

x² + 10x - 100

b)

x² + 10x + 100

c)

x² + 10x - 25

d)

x² + 10x + 25

15.

Solve by completing the square.
$x^2-8x-20=0$

a)

$x=\left\{-2,\ 10\right\}$

b)

$x=\left\{-10,\ 2\right\}$

c)

$x=\left\{-20,\ -8\right\}$

d)

$x=\left\{8,\ 20\right\}$

16.

Which of the following equations shows the vertex form of a quadratic?

a)

x = -b/2a

b)

x = (-b ±√b² - 4ac)/2a

c)

y = ax² + bx + c

d)

y = a(x - h)² + k

17.

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

18.

Which of the following equations is in vertex form?

a)

f(x) = x² + 6x - 2

b)

f(x) = (x - 1)² + 2

19.

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

20.

Factor the following:

$x^2-10x+25$

a)

$\left(x-5\right)\left(x-5\right)$

b)

$\left(x+5\right)\left(x-5\right)$

c)

$\left(x-5\right)\left(x+5\right)$

21.

Factor the following:

$x^2-6x+9$

a)

$\left(x-3\right)\left(x+3\right)$

b)

$\left(x-3\right)\left(x-3\right)$

c)

$\left(x+3\right)\left(x+3\right)$

22.

Identify the roots of the quadratic.

a)

x = {-1, 3}

b)

x = {-3}

c)

x = {1, -4}

d)

x = {1}

23.

What are the x-intercepts of the parabola?

a)

x = {0, 6}

b)

x = {-6}

c)

x = {-6, 0}

d)

x = {0}

24.

What are the solutions to the quadratic?

a)

x = {-3, -2}

b)

x = {-2.5}

c)

x = {-5}

d)

x = {-5, 0}

25.

Find the solution(s) to the quadratic equation:

x^2-81=0

a)

x = {9}

b)

x = {-9}

c)

x = {-9, 9}

d)

No solution

8.7 Complete The Square

Total questions: 25

Worksheet time: 1hrs 11mins

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