Free Printable PHS: Completing the Square for Circles

1.

Complete the square.

x² + 2x + ____

a)

x² + 2x + 1

b)

x² + 2x - 1

c)

x² + 2x + 2

d)

x² + 2x +2

2.

Find the missing value "c" to complete the square.

x² - 4x + ____

a)

4

b)

2

c)

8

d)

-4

3.

Complete the square.
x² + 6x + ____

a)

x² + 6x + 9

b)

x² + 6x - 36

c)

x² + 6x + 36

d)

x² + 6x - 9

4.

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

x_{ }^2-8x+c

a)

-4

b)

4

c)

8

d)

16

5.

Complete the Square
x² + 10x + ____

a)

x² + 10x - 100

b)

x² + 10x + 100

c)

x² + 10x - 25

d)

x² + 10x + 25

6.

Complete the square for

x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² - 12x - 36

d)

x² - 12x - 144

7.

Complete the square for

x² - 12x + ____

a)

144

b)

36

c)

- 36

d)

24

8.

Complete the square.
x² + 14x + ____

a)

x² + 14x - 196

b)

x² + 14x + 49

c)

x² + 14x - 49

d)

x² + 14x + 196

9.

Complete the square.

x² - 16x + ____

a)

8

b)

64

c)

36

d)

- 8

10.

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

k^2-18k+c

a)

81

b)

-9

c)

18

d)

9

11.

Complete the square.

x² + 20x + ____

a)

x² + 20x - 40

b)

x² + 20x + 100

c)

x² + 20x - 100

d)

x² + 20x + 40

12.

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

a^2-22a+c

a)

-121

b)

121

c)

11

d)

-11

13.

Complete the Square

x² + 24x + ____

a)

x² + 24x - 24

b)

x² + 24x + 24

c)

x² + 24x - 144

d)

x² + 24x + 144

14.

Complete the square for

x² + 26x + ____

a)

x² + 26x + 26

b)

x² + 26x + 169

c)

x² + 26x - 169

d)

x² + 26x - 26

15.

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

x^2-28x+c

a)

28

b)

14

c)

196

d)

56

16.

Complete the square for

x² + 30x + ____

a)

x² + 30x + 30

b)

x² + 30x + 225

c)

x² + 30x - 30

d)

x² + 30x - 225

17.

Find the value of "c" that completes the square. Then rewrite the trinomial as a perfect square.

x^2-2x+c

a)

$1;\ \left(x-2\right)^2$

b)

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

c)

$1;\ \left(x-1\right)^2$

d)

$4;\ \left(x-1\right)^2$

18.

Find the value of "c" that completes the square. Then rewrite the trinomial as a perfect square.

p^2+14p+c

a)

$49;\ \left(p+7\right)^2$

b)

$7;\ \left(p+7\right)^2$

c)

$49;\ \left(p+14\right)^2$

d)

$7;\ \left(p+49\right)^2$

19.

Find the value of "c" that completes the square. Then rewrite the trinomial as a perfect square.

m_{ }^2+4m+c

a)

$4;\ \left(m+4\right)^2$

b)

$2;\ \left(m+2\right)^2$

c)

$2;\ \left(m+4\right)^2$

d)

$4;\ \left(m+2\right)^2$

20.

Find the value of "c" that completes the square. Then rewrite the trinomial as a perfect square.

b^2-12b+c

a)

$36;\ \left(b+6\right)^2$

b)

$36;\ \left(b-6\right)^2$

c)

$6;\ \left(b-36\right)^2$

d)

$6;\ \left(b-6\right)^2$

21.

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

22.

Find the coefficient value of "b" that completes the perfect square. Then rewrite the trinomial as a perfect square.

m_{ }^2+bm+36

a)

$18;\ \left(m+36\right)^2$

b)

$6;\ \left(m+18\right)^2$

c)

$12;\ \left(m+6\right)^2$

d)

$24;\ \left(m+144\right)^2$

23.

Find the value of "c" that completes the square. Then rewrite the trinomial as a perfect square.

m_{ }^2+10m+c

a)

$10;\ \left(m+5\right)^2$

b)

$25;\ \left(m+5\right)^2$

c)

$10;\ \left(m+10\right)^2$

d)

$25;\ \left(m+10\right)^2$

24.

What does (h,k) stand for in the standard circle equation?

a)

(h,k) is the center of the circle

b)

(h,k) is a point on the circle.

c)

(h,k) is a point that we guess and find

d)

(h,k) is the distance of the circle

25.

What does r in the standard circle equation stand for?

a)

r is the distance of the circle

b)

r is the radius of the circle

c)

r is the x coordinate of the center of the circle

d)

r is the y coordinate of the center of the circle

PHS: Completing the Square for Circles

Total questions: 25

Worksheet time: 19mins

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