Free Printable Quadratic Functions Review

1.

Find the vertex of

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

a)

$\left(2,3\right)$

b)

$\left(-2,3\right)$

c)

$\left(2,-3\right)$

d)

$\left(-2,-3\right)$

2.

Find the vertex form of

f\left(x\right)=2x^2-8x+1

a)

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

b)

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

c)

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

d)

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

3.

Find the x-intercepts of

f\left(x\right)=x^2-11x+30

a)

$x=5,6$

b)

$x=-6,-5$

c)

$x=-15,2$

d)

$x=-2,15$

4.

Find the y-intercept of

f\left(x\right)=x^2-11x+30

a)

30

b)

-30

c)

11

d)

-11

5.

What is the range of this function?

a)

(- ∞,+∞)

b)

[0, +∞)

c)

[-2, +∞)

d)

[2, +∞)

6.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

7.

Which equation best represents the graph?

a)

y = 2(x - 4)² + 5

b)

y = 2(x + 4)² + 5

c)

y = -2(x - 4)² + 5

d)

y = -2(x + 4)² + 5

8.

Solve:
2x² - 9x = 35

a)

x = 7/2, x = -6

b)

x = -5/2, x =5

c)

x = -3/7, x =6

d)

x = -5/2, x = 7

9.

Find the missing value "c" to create a perfect square trinomial:
x² – 8x + ___

a)

-4

b)

16

c)

4

d)

8

10.

Convert to vertex form:
f(x) = x² + 10x + 24

a)

f(x) = ( x - 5 )² + 1

b)

f(x) = ( x + 5 )² - 1

c)

f(x) = ( x - 5 )² - 1

d)

f(x) = ( x + 5 )² + 1

11.

Write the equation of the quadratic in standard form given the following:
axis of symmetry: x=1
Points: (2, 5) (-2, 21)

a)

f(x)=(x-1)²+5

b)

f(x)=1/2(x-1)²+3

c)

f(x)=2(x-1)²+3

d)

f(x)=2(x-1)²-3

12.

Write the equation of the quadratic in vertex form given the following:
vertex: (4, -2)
point: (0,-6)
opens down

a)

f(x)=(x-4)²-2

b)

f(x)=-4(x-4)²-2

c)

f(x)=1/4(x+4)²-2

d)

f(x)=-1/4(x-4)²-2

13.

The height of a rocket, at selected times, is shown in the table above.

Based on these data, which statement is not a valid conclusion?

a)

The rocket was launched from a height of 180 feet.

b)

The maximum height of the rocket occurred 3 seconds after launch.

c)

The rocket was in the air approximately 6 seconds before hitting the ground.

d)

The rocket was above 300 feet for approximately 2 seconds.

14.

Morgan throws a ball up into the air. The height of the ball above the ground, in feet, is modeled by the function h(t) = −16t² + 24t, where t represents the time, in seconds, since the ball was thrown. What is the appropriate domain for this situation?

a)

$0\le t\le1.5$

b)

$0\le t\le9$

c)

$0\le h\left(t\right)\le1.5$

d)

$0\le h\left(t\right)\le9$

15.

A ball is thrown into the air from the edge of a 48-foot-high cliff so that it eventually lands on the ground. The graph below shows the height, y, of the ball from the ground after x seconds.

For which interval is the ball's height always decreasing?

a)

$0\le x\le2.5$

b)

$0<x<5.5$

c)

$2.5<x<5.5$

d)

$x\ge2$

16.

An archer shoots an arrow into the air such that its height at any time, t, is given by the function h(t) = -16t²+ kt + 3. If the maximum height of the arrow occurs at time t = 4, what is the value of k?

a)

128

b)

64

c)

8

d)

4

17.

The expression -4.9t² + 50t + 2 represents the height, in meters, of a toy rocket t seconds after launch. The initial height of the rocket, in meters, is

a)

0

b)

2

c)

4.9

d)

50

18.

A ball is thrown straight up at an initial velocity of 54 feet per second. The height of the ball t seconds after it is thrown is given by the formula h(t) = 54t − 12t² .

How many seconds after the ball is thrown will it return to the ground?

a)

9.2

b)

6

c)

4.5

d)

4

19.

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function:

p= -15x² +600x +60

What is the maximum profit you can make from selling tickets?

a)

$6060

b)

$20

c)

$600

d)

$10,250

20.

If you square 5 more than a positive number, the result is 88 more than 12 times the number. Find the numbers.

a)

-9, 7

b)

√75

c)

9, -7

d)

15, -5

21.

The product of two consecutive negative even integers is 24. Find the integers.

a)

6, 8

b)

6, 4

c)

-6, -8

d)

-6, -4

22.

The area of a playground is 336 yd2 . The width of the playground is 5 yd longer than its length. Find the length and width of the playground

a)

length = 26 yd, width = 21 yd

b)

length = 21 yd, width = 26 yd

c)

length = 21 yd, width = 16 yd

d)

length = 16 yd, width = 21 yd

23.

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function p= -15x² +600x +60 , where x is the price of each ticket. What is the maximum profit you can make from selling tickets?

a)

$6060

b)

$20

c)

$600

d)

$10,250

24.

A rectangle has an area of 24 square units. The width is 5 units less than the length. What is the length, in units, of the rectangle?

a)

6

b)

8

c)

3

d)

19

Quadratic Functions Review

Total questions: 24

Worksheet time: 4hrs 0mins

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