Free Printable COMPLETE THE SQUARE

1.

Convert to vertex form:

y = x² + 4x + 10

a)

y = (x + 4)² + 6

b)

y = (x + 2)² + 6

c)

y = (x + 4)² - 6

d)

y = (x + 2)² - 6

2.

Convert to vertex form:

y = x² + 8x + 2

a)

y = (x + 4)² - 14

b)

y = (x + 4)² - 6

c)

y = (x + 4)² - 18

d)

y = (x + 4)² + 6

3.

Convert to vertex form:

y = x² + 8x - 1

a)

y = (x + 4)² - 17

b)

y = (x + 4)² - 16

c)

y = (x + 4)² - 9

d)

y = (x + 4)² - 15

4.

Convert to vertex form:

y = x² - 2x + 5

a)

y = (x - 1)² + 4

b)

y = (x - 1)² - 4

c)

y = (x - 1)² + 3

d)

y = (x - 1)² + 7

5.

Convert to vertex form:

y = x² + 10x + 23

a)

y = (x + 5)² - 2

b)

y = (x + 5)² + 2

c)

y = (x + 5)² + 13

d)

y = (x + 5)² - 13

6.

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

7.

Convert to vertex form:

y = x² + 4x + 9

a)

y = (x + 2)² + 5

b)

y = (x - 2)² + 5

c)

y = (x + 4)² + 5

d)

y = (x + 2)² - 5

8.

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

9.

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

10.

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

11.

Given the perfect square trinomial, identify the equivalent expression

x²-18x+81

a)

(x-18)²

b)

(x-9)²

c)

(x+81)²

d)

(x+9)²

12.

Given the perfect square trinomial, identify the equivalent expression

x²+14x+49

a)

(x+14)²

b)

(x+49)²

c)

(x-7)²

d)

(x+7)²

13.

What should be added to both sides of the following equation to complete the square?
x² + 12x = 5

a)

12

b)

6

c)

36

d)

5

14.

We use $\left(\frac{b}{2}\right)^2$ to complete the square?

a)

No

b)

Maybe

c)

I don't know

d)

Yes

15.

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

16.

Complete the Square
x² + 6x + 20

a)

(x + 3x)² + 11

b)

(x + 3)² + 11

c)

(x + 6)² + 11

d)

(x + 3)² + 29

17.

Complete the Square
x² + 6x + 5

a)

(x + 3)² - 4

b)

(x + 6)² - 4

c)

(x + 3x)² - 4

d)

(x + 3)² + 9

18.

When Factoring x² - 4x + 4 = 20,

what goes in the blank? (Hint: use complete the square)

(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

19.

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

20.

What should be added to both sides of the following equation to complete the square?
x² + 12x = 5

a)

12

b)

6

c)

36

d)

5

21.

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}

22.

Solve by completing the square:
v² + 6v − 59 = 0

a)

{-5 + 5√2, -5 - 5√2}

b)

{5 + 5√2, 5 - 5√2}

c)

{-3 + 2√17, -3 - 2√17}

d)

{3 + 2√17, 3 - 2√17}

23.

Determine the equation of the circle in standard form: x²+ y²+ 6x - 12y + 20 = 0

a)

(x-3)² + (y+6)² = 25

b)

(x+3)² + (y-6)² = 25

c)

(x-3)² + (y+6)² = 45

d)

(x+3)² + (y-6)² = 5

24.

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

a)

4

b)

2

c)

8

d)

20

25.

Solve by taking the Square Root:

16a² - 9 = 0

a)

a = ± ³/₄

b)

a = ± ⁴/₃

c)

a = ± ⁹/₁₆

d)

a = ± ¹⁶/₉

26.

Solve by taking the Square Root:

4m² - 100 = 0

a)

m = ± 25

b)

m = 96

c)

m = ± 5

d)

m = -96

27.

Solve for x by taking the Square Root:

(x+6)²= 49

a)

x = 7 and 12

b)

x = ±7

c)

x = 1 and -13

d)

x = 43 and -55

28.

Solve the equation using square roots:

x² = 121

a)

x = 60.5

b)

x = ± 11

c)

x = ± 12

d)

x= 11

29.

Solve by completing the square:

n² - 2n - 3 = 0

a)

n = 3 and -1

b)

n = 4 and -4

c)

n = 5 and -3

d)

n = 8 and -7

30.

Solve by completing the square:

x² + 10x = -9

a)

x = 1 and -12

b)

x = -1 and -9

c)

x = 1 and -9

d)

x = 1 and -1

31.

Solve by completing the square:

k² − 12k + 20 = 0

a)

k = 10 and 2

b)

k = -6 and -6

c)

k = 22 and -10

d)

k = -2 and 6

32.

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}

33.

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

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)

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

34.

Solve by taking the Square Root:

16a² - 9 = 0

a)

a = ± ³/₄

b)

a = ± ⁴/₃

c)

a = ± ⁹/₁₆

d)

a = ± ¹⁶/₉

35.

Solve by taking the Square Root:

4m² - 100 = 0

a)

m = ± 25

b)

m = 96

c)

m = ± 5

d)

m = -96

36.

Solve by completing the square:

k² − 12k + 20 = 0

a)

k = 10 and 2

b)

k = -6 and -6

c)

k = 22 and -10

d)

k = -2 and 6

37.

Solve by completing the square.
$x^2-12x+20=0$

a)

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

b)

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

c)

$x=\left\{-12,\ 20\right\}$

d)

$x=\left\{12,\ 20\right\}$

38.

Solve by completing the square.
$x^2-6x-27=0$

a)

$x=\left\{-9,\ -3\right\}$

b)

$x=\left\{-3,\ 9\right\}$

c)

$x=\left\{-9,\ 3\right\}$

d)

$x=\left\{3,\ 9\right\}$

39.

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

40.

What is one of the solutions to this equation?

(x - 3)² = 49

a)

7

b)

-7

c)

-4

d)

4

41.

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

42.

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

43.

When factoring $x^2-10x+25\ =\ 49$
what goes into the blank $\left(x-\ldots\right)^2=49$

a)

5

b)

10

c)

7

d)

25

44.

Solve the equation using square roots:

x² = 121

a)

x = 60.5

b)

x = ± 11

c)

x = ± 12

d)

x= 11

45.

Solve by completing the square:

n² - 2n - 3 = 0

a)

n = 3 and -1

b)

n = 4 and -4

c)

n = 5 and -3

d)

n = 8 and -7

46.

Factor the perfect square trinomial:
x² + 16x + 64

a)

(x+8)²

b)

(x-8)²

c)

(x-4)²

d)

(x+4)²

47.

Factor the perfect square trinomial
x² + 14x + 49

a)

(x+7)²

b)

(x+7)(x-7)

c)

(x-7)²

d)

(x+14)²

48.

Factor the perfect square trinomial
x² - 6x + 9

a)

(x-3)²

b)

(x+3)²

c)

(x+3)(x-3)

d)

(x+9)²

49.

Is this a perfect square trinomial?
x² - 20x + 100

a)

(x+10)²

b)

(x-10)²

c)

(x+20)²

d)

(x+10)(x-10)

50.

Is this a perfect square trinomial?
x² + 18x + 9

a)

Yes

b)

No

51.

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

52.

Which function is equivalent to
y = x² - 6x + 10?

a)

y = (x + 3)² - 1

b)

y = (x - 3)² + 1

c)

y = (x + 6)² - 10

d)

y = (x - 6)² + 10

53.

Convert the equation y= x²+ 4x + 11 into vertex form.

a)

y = (x + 2)² - 4

b)

y = (x + 2)² + 7

c)

y = (x + 2)²

d)

y = (x - 2)² - 7

54.

Complete the square:

$x^2+6x\ =\ 0$

a)

$\left(x+3\right)^2=9$

b)

$\left(x+3\right)^2=3$

c)

$\left(x+3\right)^2=6$

d)

$\left(x+6\right)^2=36$

55.

Complete the square:

$y^2+4y\ +3=\ 0$

a)

$\left(y+2\right)^2=1$

b)

$\left(y+2\right)^2=4$

c)

$\left(y+2\right)^2=-3$

d)

$\left(y+4\right)^2=13$

56.

Complete the Square and write in Vertex Form:
f(x) = x² + 6x + 5

a)

(x + 3)² - 4

b)

(x + 6)² - 4

c)

(x + 3x)² - 4

d)

(x + 3)² + 9

57.

Convert to vertex form:

y = x² + 10x + 23

a)

y = (x + 5)² - 2

b)

y = (x + 5)² + 2

c)

y = (x + 5)² + 13

d)

y = (x + 5)² - 13

58.

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

59.

Convert to vertex form:

y\ =\ 6x^2+12x+13

a)

$y=6\left(x+1\right)^2-7$

b)

$y\ =\ \left(6x+6\right)^2-42$

c)

$y=\left(x-6\right)^2+7$

d)

$y=\frac{13}{6}\left(x+1\right)^2+7$

60.

$y=-3(x+5)^2-4$
Convert the equation from vertex form to standard form.

a)

y = 9x²- 15x + 21

b)

y = -3x²- 75x - 4

c)

y = 9x²+ 90x + 221

d)

y = -3x²- 30x - 79

61.

$y=-\frac{2}{3}(x-9)^2-2$
Convert the equation from vertex form to standard form

a)

$y=-\frac{2}{3}x^2-12x-52$

b)

$y=-\frac{2}{3}x^2+12x-56$

c)

$y=-\frac{2}{3}x^2+18x-56$

d)

$y=-\frac{2}{3}x^2-18x+52$

62.

Convert the equation y= x²+ 4x + 11 into vertex form.

a)

y = (x + 2)² - 4

b)

y = (x + 2)² + 7

c)

y = (x + 2)²

d)

y = (x - 2)² - 7

63.

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

64.

Factor the perfect square trinomial:
x² + 16x + 64

a)

(x+8)²

b)

(x-8)²

c)

(x-4)²

d)

(x+4)²

65.

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

a)

36

b)

24

c)

144

d)

-36

66.

Factor the perfect square trinomial
x² + 14x + 49

a)

(x+7)²

b)

(x+7)(x-7)

c)

(x-7)²

d)

(x+14)²

67.

Factor: x² - 4x + 4

a)

(x + 2)²

b)

(x - 2)²

c)

(x + 4)²

d)

(x - 4)²

68.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

69.

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

a)

4

b)

2

c)

8

d)

20

70.

Convert to vertex form:

y = x² + 4x + 10

a)

y = (x + 4)² + 6

b)

y = (x + 2)² + 6

c)

y = (x + 4)² - 6

d)

y = (x + 2)² - 6

71.

Factor the following perfect square trinomial using the rule(b/2)² :

x² + 18x + 81

a)

(x + 9)(x – 9)

b)

(x + 18)²

c)

(x + 9)²

d)

(x + 6)²

72.

Write the following quadratic expression in completed square form...

x² + 8x - 1

a)

(x + 4)² - 17

b)

(x + 4)² - 16

c)

(x + 4)² - 9

d)

(x + 4)² - 15

73.

Solve by completing the square. Round.
x² -4x = 5

a)

11 and -7

b)

1 and 3

c)

1.73 and -1.73

d)

5 and -1

74.

Factor: 49x² - 100

a)

(49x + 100)(x - 1)

b)

(7x - 10)(7x + 10)

c)

(49x - 10)(x + 10)

d)

(7x -10)(7x - 10)

75.

Use the quadratic formula to solve $2x^2+2x-12$

a)

-2, 3

b)

2, 3

c)

2, -3

d)

-2, -3

76.

Solve by completing the square. $y^2+10y+9=0$

a)

1 and -12

b)

-1 and -9

c)

1 and -9

d)

1 and -1

77.

Determine the values of a, b, and c for the quadratic equation: $4x^2-8x-3=0$

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

78.

Solve using the quadratic formula. $2x^2-9x-35=0$

a)

x = 7/2, x = -6

b)

x = -5/2, x =5

c)

x = -3/7, x =6

d)

x = -5/2, x = 7

79.

Solve by completing the square.
$x^2-6x-27=0$

a)

$\left(x+3\right)^2=21$

b)

$\left(x-3\right)^2=36$

c)

$\left(x-6\right)^2=36$

d)

$\left(x+6\right)^2=21$

80.

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

81.

Convert to vertex form:

y = x² - 2x + 5

a)

y = (x - 1)² + 4

b)

y = (x - 1)² - 4

c)

y = (x - 1)² + 3

d)

y = (x - 1)² + 7

82.

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

83.

Convert to vertex form.
y = 3x² +6x - 5

a)

y=3(x+1)² - 8

b)

y=3(x-1)² - 8

c)

y=3(x+2)² - 8

d)

y=3(x-2)² - 8

84.

Convert to vertex form:

y\ =\ 6x^2+12x+13

a)

$y=6\left(x+1\right)^2-7$

b)

$y\ =\ \left(6x+6\right)^2-42$

c)

$y=\left(x-6\right)^2+7$

d)

$y=\frac{13}{6}\left(x+1\right)^2+7$

85.

Complete the square and write in Vertex Form

2x² - 16x - 5 = 1

a)

(x - 4)² = 6

b)

(x - 4)² = 38

c)

(x - 4)² = 14

d)

(x - 4)² = 19

86.

Complete the square and write in Vertex Form

3x² - 12x - 5 = 0

a)

3(x - 2)² = 17

b)

3(x - 2)² = 15

c)

3(x - 2)² = 75

d)

3(x - 2)² = 9

87.

Complete the square and write in Vertex Form

5x² - 30x - 2 = 0

a)

5(x - 30)² = 17

b)

5(x - 3)² = 47

c)

5(x - 3)² = 15

d)

5(x - 6)² = 30

88.

Complete the square and write in Vertex Form

4x² + 8x - 33 = 0

a)

4(x - 1)² = 33

b)

4(x - 1)² = 47

c)

4(x - 1)² = 37

d)

4(x - 1)² = 29

89.

Complete the Square:
$x^2-14x+47=0$

a)

$\left(x-7\right)^2=10$

b)

$\left(x+7\right)^2=88$

c)

$\left(x-49\right)^2=7$

90.

Complete the Square:
$x^2=10x-1$

a)

$\left(x+5\right)^2=24$

b)

$\left(x-5\right)^2=24$

c)

$\left(x-1\right)^2=10$

91.

Complete the Square Step: Step 3
x²+ 6x + 9 = 40 + 9

a)

(x + 3) (x - 3) = 49

b)

(x + 3)² = 31

c)

(x - 3)² = 49

d)

(x + 3)² = 49

92.

Complete the Square Step: Step 4 - Solving

(x - 3)² = 49

a)

x - 3 = 49

b)

x - 3 = ±7

c)

x - 3 = 24.5

d)

x - 3 = 7

93.

Complete the Square Step: Step 5 - Solving

x - 3 = ±7

a)

x = 10, -7

b)

x = 4, -10

c)

x = 10

d)

x = 4

94.

Complete the Square and write in Vertex Form:
f(x) = x² + 6x + 5

a)

(x + 3)² - 4

b)

(x + 6)² - 4

c)

(x + 3x)² - 4

d)

(x + 3)² + 9

95.

Convert the equation y= x²- 2x - 5 into vertex form.

a)

y= (x - 1)²- 6

b)

y= - (x - 1)²- 6

c)

y= (x + 1)²- 6

d)

y= - (x + 6)²- 1

96.

Complete the square and write in Vertex Form

x² + 6x = 5

a)

(x + 3)² = 5

b)

(x + 6)² = 9

c)

(x + 3)² = 14

d)

(x + 6)² = 14

97.

Complete the square and write in Vertex Form

x² - 14x = 5

a)

(x - 7)² = 5

b)

(x - 7)² = 54

c)

(x - 7)² = 14

d)

(x - 7)² = 49

98.

Complete the Square

2 (x²+ 12x + ___ ) = -64 + ___

a)

2 (x²+ 12x + _36_ ) = 72

b)

2 (x²+ 12x + _36_ ) = 36

c)

2 (x²+ 12x + _36_ ) = 12

d)

2 (x²+ 12x + _36_ ) = 8

99.

Complete the Square

4 (x²+ 8x + ___ )= -20 + ___

a)

4 (x²+ 8x + _16 )= -20 + 16_

b)

4 (x²+ 8x + _16 )= -20 + 64_

c)

4 (x²+ 8x + _4 )= -20 + 16_

d)

4 (x²+ 8x + _2 )= -20 + 8_

100.

Complete the Square

3 (x²+ 6x + ___ )= 40 + ___

a)

3 (x²+ 6x + _36 )= 40 + 36_

b)

3 (x²+ 6x + _9 )= 40 + _9_

c)

3 (x²+ 6x + _9_ )= 40 + 27_

d)

3 (x²+ 6x + _3_ )= 40 + _9_

101.

Complete the square and write in Vertex Form

5x² - 30x = 2

a)

5(x - 30)² = 17

b)

5(x - 3)² = 47

c)

5(x - 3)² = 15

d)

5(x - 6)² = 30

102.

Complete the square and write in Vertex Form

3x² - 12x = 5

a)

3(x - 2)² = 17

b)

3(x - 2)² = 15

c)

3(x - 2)² = 75

d)

3(x - 2)² = 9

103.

Complete the square and write in Vertex Form

4x² + 8x - 33 = 0

a)

4(x - 1)² = 33

b)

4(x - 1)² = 47

c)

4(x - 1)² = 37

d)

4(x - 1)² = 29

104.

Solve by completing the square. Round.
x² -4x = 5

a)

11 and -7

b)

1 and 3

c)

1.73 and -1.73

d)

5 and -1

105.

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

106.

Solve by completing the square.
$x^2-6x-59=0$

a)

$x=\left\{\pm2\sqrt{17}+3\right\}$

b)

$x=\left\{\pm17\sqrt{2}+3\right\}$

c)

$x=\left\{\pm2\sqrt{17}-3\right\}$

d)

$x=\left\{\pm17\sqrt{2}-3\right\}$

107.

Factor the perfect square trinomial
x² + 14x + 49

a)

(x+7)²

b)

(x+7)(x-7)

c)

(x-7)²

d)

(x+14)²

108.

$n^2-10n+24=0$

Solve this equation by factoring

a)

$\left\{8,3\right\}$

b)

$\left\{4,6\right\}$

c)

$\left\{-4,-6\right\}$

COMPLETE THE SQUARE

Total questions: 108

Worksheet time: 2hrs 48mins

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