Free Printable COMPLETING THE SQUARE

1.

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)

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

2.

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)

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

3.

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)

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

4.

Solve by completing the square.
$x^2-14x-15=0$

a)

$x=\left\{1,\ 15\right\}$

b)

$x=\left\{-15,\ -1\right\}$

c)

$x=\left\{-15,\ 1\right\}$

d)

$x=\left\{-1,\ 15\right\}$

5.

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)

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

6.

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

7.

What is the vertex of y=x²+4x+3?

a)

(2,1)

b)

(-2,1)

c)

(0,0)

d)

(-2,-1)

8.

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

9.

Determine the vertex of the parabola y=5(x-2)²–7

a)

(5, -7)

b)

(-2, -7)

c)

(2, -7)

d)

(-7, -2)

10.

What is the vertex of y=x²+4x+3?

a)

(2,1)

b)

(-2,1)

c)

(0,0)

d)

(-2,-1)

11.

Solve the equation by completing the square.

-x^2-2x+5=0

a)

$x=-1\pm2i$

b)

$x=1\pm2i$

c)

$x=-2\pm i$

d)

$x=-1\pm i\sqrt{2}$

12.

Solve the equation by completing the square.

x^2+6x+22=0

a)

$x=3\pm i\sqrt{13}$

b)

$x=-3\pm3i\sqrt{10}$

c)

$x=3\pm3i\sqrt{10}$

d)

$x=-3\pm i\sqrt{13}$

13.

Write in vertex form

y=-x^2+4x-1

a)

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

b)

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

c)

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

d)

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

14.

Write in vertex form

y=2x^2-8x+1

a)

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

b)

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

c)

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

d)

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

15.

The profit P from handmade sweaters depends on the price s at which each sweater is sold. The function

P=-s^2+120s-2000

models the monthly profit from sweaters for one custom tailor. What is the maximum monthly profit, in dollars, determined by this model?

Hint: Write the function in vertex form.

a)

A price of $60 per sweater gives a maximum monthly profit of $1600.

b)

A price of $70 per sweater gives a maximum monthly profit of $1800.

c)

A price of $50 per sweater gives a maximum monthly profit of $1500.

d)

A price of $80 per sweater gives a maximum monthly profit of $2100.

16.

An electronic company has a new line of headphones with bluetooth. Their research suggests that the daily sales s for the new product can be modeled by

s=-p^2+120p+1400,

where p is the price of each unit. What price gives maximum daily sales and what are the maximum daily sales?

a)

A price of $70 per headphone gives a maximum daily sales of $7000.

b)

A price of $60 per headphone gives a maximum daily sales of $4500.

c)

A price of $60 per headphone gives a maximum daily sales of $5000.

d)

A price of $70 per headphone gives a maximum daily sales of $5500.

17.

The height of a punted football can be modeled with the quadratic function

h=-0.01x^2+1.18x+2.

the horizontal distance in feet from the point of impact with the kicker's foot is x, and h is the height of the football in feet.
Find the vertex of the graph by completing the square.

a)

(58, 35.71)

b)

(59, 36.81)

c)

(59, 35.81)

d)

(58, 36.81)

18.

The height of a punted football can be modeled with the quadratic function

h=−0.01x^2+1.18x+2.

the horizontal distance in feet from the point of impact with the kicker's foot is x, and h is the height of the football in feet.Find the vertex of the graph by completing the square. The nearest defensive player is 5 ft. horizontally from the point of impact. How high must the player reach to block the punt?

a)

7.65 ft

b)

7.55 ft

c)

8.65 ft

d)

7.45 ft

COMPLETING THE SQUARE

Total questions: 18

Worksheet time: 5hrs 30mins

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