Free Printable Algebra Semester 2 Final Review

1.

The graph represents Andre's distance from his bike as he walks in a park. True or false: the graph has multiple horizontal intercepts?

a)

True

b)

False

2.

The graph represents Andre's distance from his bike as he walks in a park. True or false: a horizontal intercept of the graph represents when Andre was with his bike?

a)

True

b)

False

3.

The graph represents Andre's distance from his bike as he walks in a park. True or false: a minimum of the graph was (17,1)?

a)

True

b)

False

4.

The graph represents Andre's distance from his bike as he walks in a park. True or false: the graph has 2 maximums?

a)

True

b)

False

5.

The graph represents Andre's distance from his bike as he walks in a park. True or false: about 21 seconds after he left his bike, he was farthest away from it, at about 8.3 feet?

a)

True

b)

False

6.

Function f is defined by f(x) = x². What is f(2)?

a)

2

b)

4

c)

8

d)

16

7.

Function f is defined by f(x) = x². What is f(3)?

a)

9

b)

6

c)

5

d)

27

8.

Match the feature with the corresponding statement in function notation:
maximum height

a)

h(0) = 7

b)

h(1.5)

c)

h(4)

d)

h(t) = 6 for $7\le t\le8$

9.

Match the feature with the corresponding statement in function notation:
minimum height

a)

h(0) = 7

b)

h(1.5)

c)

h(4)

d)

h(t) = 6 for $7\le t\le8$

10.

Match the feature with the corresponding statement in function notation:
height staying the same

a)

h(0) = 7

b)

h(1.5)

c)

h(4)

d)

h(t) = 6 for $7\le t\le8$

11.

Match the feature with the corresponding statement in function notation:
starting height

a)

h(0) = 7

b)

h(1.5)

c)

h(4)

d)

h(t) = 6 for $7\le t\le8$

12.

The temperature was recorded at multiple times during the day. Function T gives the temperature n hours since midnight. Decide if the rate of change is positive, negative, or 0 for the time period from n = 1 to n = 5.

a)

Positive

b)

Negative

c)

Zero

13.

The temperature was recorded at multiple times during the day. Function T gives the temperature n hours since midnight. Decide if the rate of change is positive, negative, or 0 for the time period from n = 5 to n = 7.

a)

Positive

b)

Negative

c)

Zero

14.

The temperature was recorded at multiple times during the day. Function T gives the temperature n hours since midnight. Decide if the rate of change is positive, negative, or 0 for the time period from n = 15 to n = 18.

a)

Positive

b)

Negative

c)

Zero

15.

The graph shows the total distance, in feet, walked by a person as a function of time, in seconds. Was the person walking faster between 20 - 40 seconds or 80 - 100 seconds?

a)

20 - 40 seconds

b)

80 - 100 seconds

c)

neither

d)

they're equal

16.

The function P shown in the table gives the percent of voters between 18 to 29 years old that participated in election year t. Determine the average rate of change for P between 1992 and 2000.

a)

.1205%

b)

.0125%

c)

10.25%

d)

1.025%

17.

The height of a squirrel running up and down a tree is a function of time. Match the description with the statement about average rate of change of the function for that interval.

The squirrel runs up the tree very fast.

a)

The average rate of change is negative

b)

The average rate of change is zero

c)

The average rate of change is small and positive

d)

The average rate of change is large and positive

18.

The height of a squirrel running up and down a tree is a function of time. Match the description with the statement about average rate of change of the function for that interval.

The squirrel starts and ends at the same height.

a)

The average rate of change is negative

b)

The average rate of change is zero

c)

The average rate of change is small and positive

d)

The average rate of change is large and positive

19.

The height of a squirrel running up and down a tree is a function of time. Match the description with the statement about average rate of change of the function for that interval.

The squirrel runs down the tree.

a)

The average rate of change is negative

b)

The average rate of change is zero

c)

The average rate of change is small and positive

d)

The average rate of change is large and positive

20.

The height of a squirrel running up and down a tree is a function of time. Match the description with the statement about average rate of change of the function for that interval.

The squirrel runs up the tree slowly.

a)

The average rate of change is negative

b)

The average rate of change is zero

c)

The average rate of change is small and positive

d)

The average rate of change is large and positive

21.

Here are the equations that define 3 functions:

f(x) = 4x-5, g(x) = 4(x - 5), h(x) = (x/4) - 5

Which function value is the largest?

a)

f(100)

b)

g(100)

c)

h(100)

d)

f(100) and h(100) are the same

e)

all three

22.

Here are the equations that define 3 functions:

f(x) = 4x-5, g(x) = 4(x - 5), h(x) = (x/4) - 5

Which function value is the largest?

a)

f(-100)

b)

g(-100)

c)

h(-100)

d)

f(-100) and g(-100) are the same

e)

all three

23.

What is Mrs. Gordon's rate from 0 to 2 seconds?

a)

2.5 feet per second

b)

.4 feet per second

c)

5 feet per second

d)

.2 feet per second

24.

Calculate the average rate of change from 20 to 40 minutes.

a)

-2 minutes per gallon

b)

-20 minutes per gallon

c)

-2 gallons per minute

d)

-20 gallons per minute

25.

A man is climbing down from 100 feet high descending 30 feet per minute. What is the rate of change?

a)

-30

b)

30

c)

100

d)

-100

26.

Identify the average rate of change (slope) between the given two points.

\left(-1,-1\right)\ and\ \left(3,7\right)

a)

$m=\frac{1}{2}$

b)

$m=-1$

c)

$m=2$

d)

$m=3$

27.

Identify the average rate of change (slope) between the given two points.

\left(-12,-18\right)\ and\ \left(-5,\ -4\right)

a)

$m=-\frac{1}{2}$

b)

$m=\frac{1}{2}$

c)

$m=-2$

d)

$m=2$

28.

What is the rate of change for the following graph?

a)

80

b)

20

c)

40

d)

160

29.

Who has the same rate of change?

a)

Dennis and Kameron have the same rate of change.

b)

Myriah and Kameron have the same rate of change.

c)

Dennis and Myriah have the same rate of change.

d)

They ALL have the same rate of change

30.

Who has the greater rate of change?

a)

Smith has the greater rate of change.

b)

Harmon has the greater rate of change.

c)

Macey has the greater rate of change.

d)

They have the same rate of change

31.

Which equation has the largest growth factor?

a)

b)

c)

d)

32.

Match the graph with the given situation: An Amazon stock doubles its value each fiscal quarter.

a)

b)

c)

d)

33.

Match the graph with the given situation: A Facebook stock decreases its value by $20 each fiscal quarter

a)

b)

c)

d)

34.

Match the graph with the given situation: A Starbucks stock increases in value by $50 each fiscal quarter

a)

b)

c)

d)

35.

Match the graph with the given situation: A Blockbuster stocks value decreases by half each fiscal quarter.

a)

b)

c)

d)

36.

New York City traditionally has an issue with rats. Starting in the year 2000 the City of New York began to take data on the rat population of a particular subway stop in Brooklyn. In the year 2000, how many rats were reported to be at the Brooklyn Train Station?

a)

32

b)

64

c)

128

d)

256

37.

New York City traditionally has an issue with rats. Starting in the year 2000 the City of New York began to take data on the rat population of a particular subway stop in Brooklyn. Based on the table above, what is the growth factor of the rats from year to year?

a)

1/2

b)

1

c)

2

d)

3

38.

New York City traditionally has an issue with rats. Starting in the year 2000 the City of New York began to take data on the rat population of a particular subway stop in Brooklyn.

Write an equation using the variable r to represent the rat population and x to represent the number of years.

a)

r(x) = 32(2)^x

b)

r(x) = 32(1/2)^x

c)

r(x) = 256(2)^x

d)

r(x) = 256(1/2)^x

39.

Write an equation for this situation: An asteroid is going through the Milky Way traveling 2,000 kilometers per hour, k. The asteroid’s speed doubles every year, y.

a)

y = 2(2,000)^k

b)

y = 2,000(1/2)^k

c)

y = 2,000(2)^k

d)

y = 1/2(2,000)^k

40.

A colony of bacteria is currently at 35,000 bacteria b, its population decreases by 1/3 after every dose of antibiotics given, d. Write an equation that represents the amount of bacterial still alive after ever dose of antibiotics.

a)

b = 35,000 (2/3)^d

b)

d = 35,000 (2/3)^b

c)

b = 35,000 (1/3)^d

d)

d = 35,000 (1/3)^b

41.

A group of biologists is surveying the mice population in a forest. The equation n=20,000(0.5)^t gives the total number of mice, n, t years since the survey began.

What does the 20,000 means in this situation?

a)

The number of years surveyed

b)

The decay factor of mice per year

c)

The initial amount of mice when the survey began

42.

A group of biologists is surveying the mice population in a forest. The equation n=20,000(0.5)^t gives the total number of mice, n, t years since the survey began.

What does the (0.5) means in this situation?

a)

The number of years surveyed

b)

The decay factor of mice per year

c)

The initial amount of mice when the survey began

43.

A group of biologists is surveying the mice population in a forest. The equation n=20,000(0.5)^t gives the total number of mice, n, t years since the survey began.

What is the population of mice 2 years after the survey began?

a)

80,000

b)

40,000

c)

20,000

d)

10,000

e)

5,000

44.

A group of biologists is surveying the mice population in a forest. The equation n=20,000(0.5)^t gives the total number of mice, n, t years since the survey began.

What is the population of mice 1 year BEFORE the survey began?

a)

80,000

b)

40,000

c)

20,000

d)

10,000

e)

5,000

45.

A biologist is studying the population of ants in one colony. By his estimate the equation p(t)=2000(1.5)^t represents the population of the colony, where p is the population and t is the number of years since the original survey.

What is the value of p(0) ?

a)

889

b)

1,333

c)

2,000

d)

3,000

e)

4,500

46.

A biologist is studying the population of ants in one colony. By his estimate the equation p(t)=2000(1.5)^t represents the population of the colony, where p is the population and t is the number of years since the original survey.

What is the value of p(2) ?

a)

889

b)

1,333

c)

2,000

d)

3,000

e)

4,500

47.

A biologist is studying the population of ants in one colony. By his estimate the equation p(t)=2000(1.5)^t represents the population of the colony, where p is the population and t is the number of years since the original survey.

What is the value of p(-1) ?

a)

889

b)

1,333

c)

2,000

d)

3,000

e)

4,500

48.

A biologist is studying the population of ants in one colony. By his estimate the equation p(t)=2000(1.5)^t represents the population of the colony, where p is the population and t is the number of years since the original survey.

What is the MEANING of p(-2)=889 ?

a)

Two years after the survey started there were 889 mice.

b)

Two years before the survey started there were 889 mice.

49.

A water treatment plant is using new technology to make salt water into clean drinking water. According to their calculations, they can use the equation g=200(3)^t where g is the number of drinkable gallons in a saltwater basin and t is the number of months that pass by.

What does the value 200 represent in this equation?

a)

The exponential growth rate of the gallons of water

b)

The number of years for the gallons of water

c)

The starting value of the amount of gallons of water

50.

A water treatment plant is using new technology to make salt water into clean drinking water. According to their calculations, they can use the equation g=200(3)^t where g is the number of drinkable gallons in a saltwater basin and t is the number of months that pass by.

What does the value 3 represent in this equation?

a)

The exponential growth rate of the gallons of water per month

b)

The number of years for the gallons of water

c)

The starting value of the amount of gallons of water

51.

A water treatment plant is using new technology to make salt water into clean drinking water. According to their calculations, they can use the equation g=200(3)^t where g is the number of drinkable gallons in a saltwater basin and t is the number of months that pass by.

How much drinkable water will there be in one month?

a)

200

b)

300

c)

500

d)

600

52.

The vertical intercept shows.....

a)

the maximum height that the graph reaches.

b)

the time that the graph reaches ground level.

c)

the height that the object started at.

d)

the minimum height that the graph reaches.

53.

Which of the following statements is true about the graph shown?

a)

f(20) = 3

b)

f(20) > f(7)

c)

There is no vertical intercept.

d)

There is no horizontal intercept.

54.

Select all the options that are true.

a)

f(7) = f(20)

b)

The vertical intercept represents the height at which the object started.

c)

There are multiple relative maximums.

d)

The minimum of the graph is 10 meters

e)

f(9) < f(1)

55.

A FedEx store buys 250 cases of paper and uses 3 cases per day. Write a function to show how many cases of paper in terms of the day, p(d).

a)

p(d) = 250 + 3d

b)

p(d) = 250 - 3d

c)

p(d) = 3d

56.

Tyler is filling a bathtub with water. Function B gives the depth of the water, in inches, t minutes after he begins filling the tub. Explain the meaning of B(9) = 11.

a)

The temperature of the water is 11 after 9 minutes.

b)

The tub has 9 inches of water after 11 minutes.

c)

The tub has 11 inches of water after 9 minutes.

57.

Determine the average rate of change between the points (4, 9) and (7, 5).

a)

4/3

b)

-4/3

c)

3/4

d)

-3/4

58.

Determine the rate of change and interpret what the rate of change means in context of the table.

a)

2

b)

0.5

c)

Balloons cost $2 each

d)

2 balloons cost $1

e)

Balloons are $0.50 each

59.

Function M shows Mary's age, function J shows John's age. Select the option that is NOT true.

a)

m(2) < j(2)

b)

m(5) = j(5)

c)

j(1) < j(6)

d)

m(9) > m(7)

60.

The graph shows the height of a rocket and of a drone as a function of time. Select all true statements.

a)

The drone is decreasing in height over the interval of 5 seconds to 7 seconds.

b)

The rocket reaches a max height of 45 feet at 2 seconds.

c)

r(3) < d(3)

d)

d(2) > d(6)

e)

The rocket and drone are at the same height at approximately 4.5 seconds.

61.

Given the graph, select all the true statements.

a)

The temperature rises more quickly from noon to 3pm than it did before noon.

b)

The temperature decreased more rapidly between 7pm and 9pm than it did from 3pm and 7pm.

c)

t(12) < t(3)

d)

The maximum temperature happened at 3pm.

62.

What is the value of x when f(x) = -1 ?

a)

-2

b)

-1

c)

0

d)

1

e)

2

63.

Determine f(-1).

a)

-10

b)

-7

c)

-4

d)

-1

e)

2

64.

Determine f(4).

a)

0.5

b)

16

65.

Explain the meaning of f(4) = 16.

a)

The height is 16 feet at 4 seconds.

b)

The height is 4 feet at 16 seconds.

66.

During what interval was the height constant?

a)

Between 0 and 2 seconds.

b)

Between 4 and 6 seconds.

c)

Between 7 and 8 seconds.

67.

I feel confident for this assessment.

a)

YES!

b)

MORE YES THAN NO

c)

NO

68.

What is the vertex of the equation

y=\left(x-3\right)^2+5

a)

(-3, 5)

b)

(3, 5)

c)

(-3, -5)

d)

(3, -5)

69.

What is the vertex of the equation

y=x^2-1

a)

(0, -1)

b)

(0, 1)

c)

(1, 0)

d)

(-1, 0)

70.

What direction does the following graph open?

g\left(x\right)=-x^2+5

a)

right

b)

left

c)

down

d)

up

71.

Given the equation for this parabola:
y=-(x-4)²-3,
does this parabola have a maximum or minimum value?

a)

Maximum

b)

Minimum

72.

What is the equation of this graph?

a)

f(x) = (x -5)² + 1

b)

f(x) = (x - 1)² - 5

c)

f(x) = (x + 1)² - 5

d)

f(x) = (x + 5)² +1

73.

The graph of a quadratic function is called a

a)

Parabola

b)

Vertex

c)

Axis of Symmetry

d)

Vertex Form

74.

If the blue graph is f(x) = x²

then the red must be...

a)

g(x) = x²- 5

b)

g(x) = x²+ 5

c)

g(x) = (x - 5)²

d)

g(x) = (x + 5)²

75.

What is the y-intercept?
f(x) = -2x² + 4x - 6

a)

(0, 6)

b)

(0, -6)

c)

(6, 0)

d)

(-6, 0)

76.

.How many zeros does this parabola have?

a)

3

b)

2

c)

0

d)

1

77.

What is c in the following equation?
y=ax²+bx+c

a)

Zeroes

b)

Axis of Symmetry

c)

Direction

d)

y-intercept

78.

Comparing the functions, which is the most narrow?

a)

f(x)=3x²

b)

g(x)= -2x²

c)

h(x)=0.5x²

d)

a(x)=12x²

79.

For a graph to be wider, the a value must be

a)

Very large number, regardless of sign

b)

Very small number, regardless of sign

c)

Negative number

d)

a=0

80.

Changing the c value of a standard form quadratic (y=ax²+bx+c) transforms the graph how?

a)

Up and down

b)

Left or right

c)

Reflects over x axis

d)

Up only

e)

Creates a change in the universe that is so chaotic it creates a new galaxy

81.

Which of the following is true when the graph of f(x)=x²+4 is transformed into the graph g(x)=2x²+4

a)

The new function has more zeroes than the old function

b)

Both functions have the same vertex

c)

The function is translated up

d)

The axis of symmetry changes

82.

Which function has vertex different from f(x)=2x²+1

a)

g(x)=x²+4

b)

g(x) = 3x²+1

c)

g(x) = x²+1

d)

g(x) = -2x²+1

83.

Convert the equation y= x(x+4) into vertex form.

a)

y= (x+4)²-4

b)

y= (x-2)²+4

c)

y= (x+2)²-4

d)

y= (x+2)²

84.

What are the green dots called?

a)

axis of symmetry

b)

vertex

c)

parabola

d)

roots or x-intercepts

85.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

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

86.

Which of the following is the Factored Form of a quadratic function?

a)

f(x) = mx + b

b)

f(x) = ax² + bx + c

c)

f(x) = a(x - m)(x - n)

d)

f(x) = a(x - h)² + k

87.

What are the x-intercepts of the parabola?

y = -3(x + 5)(x - 9)

a)

(-5, 0) and (9, 0)

b)

(5,0) and (-9, 0)

c)

(5, 0) and (9, 0)

d)

(-3, 0) and (5, 0)and (-9, 0)

88.

What are the x-intercepts of the parabola?

y = ¼(x + 2)(x - 6)

a)

(-2, 0) and (6, 0)

b)

(2, 0) and (-6, 0)

c)

(-2, 6)

d)

(¼, 0) and (-2, 0) and (6, 0)

89.

State the direction of opening of the following: y = -(x+3)(x-2)

a)

Left

b)

Up

c)

Down

d)

Right

90.

Identify the x-intercepts:

y= -3(x-5)(x+5)

a)

(-3,0) and (5,0)

b)

(5,0) and (-5,0)

c)

(5,0) and (0,5)

d)

(0,5) and (0,-5)

91.

What is the equation for this parabola in factored form?

a)

y=(x+2)(x-1)

b)

y=(x-2)(x+1)

c)

y=(x-2)(x-1)

d)

y=(x+2)(x+1)

92.

In factored form you can see the ______ of the graph easily.

a)

y-intercept

b)

vertex

c)

x-intercepts

93.

What is the factored quadratic equation in the following graph?

a)

( x+ 2)(x + 6) = y

b)

x² - 8x + 12 = y

c)

(x - 2)(x - 6) = y

d)

(x - 4)(x + 4) = y

94.

Find the zeros of the function.

h\left(x\right)=\left(-2x+3\right)\left(-x+3\right)

(a)

95.

What are the zeros of the function?

$y=\frac{2}{3}\left(x+7\right)\left(x+1\right)$

(a)

96.

What is the vertex of the function?

$y=\frac{2}{3}\left(x+7\right)\left(x+1\right)$

(a)

97.

$f\left(x\right)=\left(x+4\right)\left(x-3\right)\$ This quadratic function is written in...

a)

Standard Form

b)

Factored Form

c)

Vertex Form

98.

$f\left(x\right)=3x^2$ This quadratic function is written in...

a)

Standard Form

b)

Factored Form

c)

Vertex Form

99.

Tyler wants to know HOW HIGH the soccer ball will get if he kicks it straight up in the air.

When looking at the graph on Desmos, which value should he find?

a)

x-value at the vertex

b)

y-value at the vertex

c)

where the curve hits the x-axis (positive x-intercept)

100.

Ceiran wants to know when his model rocket will HIT THE GROUND.

When looking at the graph on Desmos, which should he find?

a)

x-value at the vertex

b)

y-value at the vertex

c)

where the curve hits the x-axis (positive x-intercept)

101.

Neha is trying to find HOW MANY SECONDS it will take a golf ball TO GET TO ITS HIGHEST POINT after being hit on the golf course.

Which should she look for?

a)

x-value at the vertex

b)

y-value at the vertex

c)

where the curve hits the x-axis (positive x-intercept)

102.

Which is the best estimate for when the football hits the ground?

a)

0.5 seconds

b)

4.0 seconds

c)

1.5 seconds

d)

2.7 seconds

103.

Which best describes the HEIGHT of the football at 2 seconds?

a)

10 feet

b)

22 feet

c)

6 feet

d)

31 feet

104.

What is the vertex and what does it mean?

a)

At 1.4 seconds the football is at a maximum height of 31 ft

b)

At 31 seconds the football is at a maximum height of 1.4 ft

c)

The ball is at its maximum height at 2.7 seconds

d)

The hits the ground at 1.4 seconds.

105.

What does the Y-INTERCEPT and what does it mean?

a)

The ball is thrown from an initial height of 1.4 feet.

b)

The ball reaches a maximum height of 6 feet.

c)

The ball hits the ground at 6 seconds.

d)

The ball is thrown form an initial height of 6 feet.

106.

$y=-3(x+5)^2-4$
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

107.

$y=-5(x+2)^2-10$
Convert the equation from vertex form to standard form.

a)

y = -5x²- 20x - 30

b)

y = -5x²- 4x - 10

c)

y = 25x² + 100x + 90

d)

y = 25x² - 10x - 30

108.

$y=4(x+2)^2-8$

Convert the equation from vertex form to standard form.

a)

$y=4x^2+16x+8$

b)

$y=4x^2+16x+16$

c)

$y=16x^2+64x-8$

d)

$y=16x^2+256x+8$

109.

Which is parabola opens downward?

a)

y = x² - 5x - 4

b)

y = (x - 3)² - 8

c)

y = -3x + 2

d)

y = -x² + 2x - 7

110.

Distribute.
(x + 3)(x + 2)

a)

x² + 6x + 5

b)

x² + 8x + 6

c)

6x²+ 6

d)

x² + 5x + 6

111.

Distribute.
(x – 7)²

a)

x²– 49

b)

x²+ 14x + 49

c)

x²+ 49

d)

x²– 14x + 49

112.

Convert to standard form: $y=-2\left(x-3\right)^2+6$

a)

$y=-2x^2+12x-12$

b)

$y=-2x^2+6x+15$

c)

$y=-2x^2+12x-18$

d)

$y\ =\ -2x^2-12$

113.

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

a)

a reflection across the line x = -4

b)

a reflection across the line y = -4

c)

a translation shifting f(x) 4 units to the left

d)

a translation shifting f(x) 4 units to the right

114.

Pablo throws a ball with a path of
h = -5(t - 2)².
Maria throws a ball with a path of
h = -5(t - 2)² + 10.
Which description is reasonable for the difference in the two equations?

a)

Maria throws the ball 10 times harder than Pablo does.

b)

Maria starts her ball at a height 10 feet higher than Pablo does.

c)

Pablo throws the ball 10 times harder than Maria does.

d)

Pablo starts his ball at a height 10 feet higher than Maria does.

115.

Match the description to its equation.
Moves right 7

a)

A

b)

B

c)

C

d)

D

116.

Match the description to its equation.
Moves up 2
Moves left 4

a)

A

b)

B

c)

C

d)

D

117.

Which list orders the quadratic functions from narrowest to widest?

a)

y = x²
y = 4x²
y = 2x² - 2
y = 0.5 x²

b)

y = 0.5 x²
y = x²
y = 2x²- 2
y = 4x²

c)

y = 4x²
y = 2x²- 2
y = x²
y = 0.5 x²

d)

y = 2x² - 2
y = 4x²
y = 0.5x²
y = x²

118.

Given f(x) = ax² , if a > 1 , the graph will transform by

a)

becoming wider

b)

becoming narrower

119.

In the vertex form f(x) = a(x - h)² + k , what does the 'h' value do?

a)

Shifts the function left or right

b)

Reflection over the x-axis

c)

Vertical stretch or compression

d)

Shifts the function up or down

120.

In the vertex form f(x) = a(x - h)² + k , what does the 'k' value do?

a)

Shifts the function left or right

b)

Reflects over the x-axis

c)

Vertical stretch or compression

d)

Shifts the function up or down

121.

The height of an object thrown into the air can be modeled by the formula h(t) = -16t² + 70t + 95, where h(t) is in feet after t seconds.
What is the height of the object after 5 seconds?

a)

95 feet

b)

45 feet

c)

70 feet

d)

171.56 feet

122.

The height of an object thrown into the air can be modeled by the formula $y=-16x^2+70x+95$
, where y is in feet after x seconds.
What is the initial height of the object?

a)

70 feet

b)

95 feet

c)

149 feet

d)

-16 feet

123.

A dolphin jumps from the water at at initial velocity of 16 feet per second. The equation h = -16t² + 80t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps?

a)

1 foot

b)

5 feet

c)

96 feet

d)

100 feet

124.

Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = –16t²+ 16t + 480, where t is the time in seconds and h is the height in feet. How long does it take Jason to hit the water?

a)

-16 seconds

b)

-6 seconds

c)

0 seconds

d)

5 seconds

125.

What form is the quadratic function written in?

f(x) = 2 + 5x - 5x²

(a)

126.

What are the x-intercept(s) for the graph of the function: f(x) = (x - 2)(x + 4)

a)

(-2 , 0) (-4 , 0)

b)

(-2 , 0) (4 , 0)

c)

(2 , 0) (-4 , 0)

d)

(2 , 0) (4 , 0)

127.

What is the y-intercept for the graph of the function: f(x) = -2x² + 3x - 9

a)

(0, 9)

b)

(0, -2)

c)

(0, 2)

d)

(0, -9)

128.

Without using a graphing calculator, which quadratic form could you determine the y-intercept?

a)

Standard Form

b)

Vertex Form

c)

Factored Form

129.

What form is the quadratic function written in?

g(x) = (x - 2)(x + 4)

(a)

130.

Which quadratic function have x-intercept(s) of (-5, 0 ) and (3, 0)?

a)

f(x) = (x - 5)(x + 3)

b)

f(x) = (x + 5)(x - 3)

c)

f(x) = (x + 3)(x + 5)

d)

f(x) = 3x² + 8x - 5

131.

What form is the quadratic function written in?

h(x) = 2x²

(a)

132.

Without using a graphing calculator, which quadratic form could you determine the x-intercepts?

(a)

133.

Which quadratic function have x-intercept(s) of (2, 0 ) and (-7, 0)?

a)

f(x) = (x - 7)(x + 2)

b)

f(x) = x² + 2x - 7

c)

f(x) = (x - 2)(x - 7)

d)

f(x) = (x - 2)(x + 7)

134.

Which expression could define this quadratic function?

a)

(x - 3)(x + 1/2)

b)

(x + 3)(x + 1)

c)

(x + 3)(x - 1/2)

d)

(x - 3)(x + 1)

135.

Which of the following quadratic function(s) can represent the graph?

a)

f(x) = (x - 4)(x - 1)

b)

g(x) = (x + 4)(x - 1)

c)

h(x) = x² - 5x + 4

d)

m(x) = (x + 4)(x + 1)

136.

Select all quadratic functions that have a y-intercept of (0, 4)?

a)

y = 2x² + 4

b)

y = (x - 4)(x + 4)

c)

y = -3x² -5x - 4

d)

y = 5x + 4 + x²

137.

Identify the y-intercept.

(a)

138.

Choose the correct quadratic expression in standard form when given (x + 4)(x - 5)

a)

x² - 9x - 20

b)

x² - x - 20

c)

x² - x + 9

d)

x² + x - 20

139.

Choose the correct quadratic expression in standard form when given (x - 4)(x - 1)

a)

x² - 5x + 4

b)

x² - 5x - 5

c)

x² + 5x - 4

d)

x² + 5x + 5

140.

Select all equivalent expression(s) of (x - 5)² ?

a)

x² + 25

b)

(x + 5)(x - 5)

c)

(x - 5)(x - 5)

d)

x² - 10x + 25

141.

Select all expressions that are equivalent to 5(x + 4)(x + 4)

a)

(5x + 20)(x + 4)

b)

(5x + 4)(x + 4)

c)

5x² + 40x + 80

d)

5(x + 4)²

e)

(5x + 20)(5x + 20)

142.

Given the equation y = x² + 6x - 8, what is the y-intercept?

(a)

143.

$h\left(t\right)=-16t^2+s$ is the vertical motion model of a falling object. Use this model to find when a diver will hit the water if he is stepping off an 84 foot cliff. Answer by rounding to the hundredth of a second.

(a)

144.

$h\left(d\right)=-0.0347d^2\ +\ 0.833d$

A kangaroo's jump follows the pattern above, where h is the height in feet and d is the horizontal distance in feet. Use a graph to identify the maximum height that the kangaroo reaches?

(a)

145.

A soccer ball is struck with an initial upward velocity of 60 ft/second. The equation to models its vertical motion is $h\left(t\right)=-16t^2+60t$ . Use a graph to figure out how long will it take the ball to return to the ground?

a)

0.27 seconds

b)

1.875 seconds

c)

3.75 seconds

d)

16 seconds

146.

$h\left(t\right)=-6t^2\ +\ s$
The height h (in feet) of a falling object on Mars after t seconds is given by the equation above, where s is the initial height in feet from which the object was dropped. A rock is dropped from a space probe from a height of 90 ft. About how many seconds, rounding to the hundredth, would it take to reach Mar's surface?

(a)

147.

Mr. Peddy was tossing softballs to his daughter, Kristin, for hitting practice. What can you tell me about this situation given the equation: $h\left(t\right)=-16t^2+15t+4$

a)

The ball left his hand 15 feet above the ground

b)

He threw the ball 16 feet per second

c)

The ball left his hand 4 feet above the ground

d)

He threw the ball 4 feet per second

e)

He threw the ball 15 feet per second

148.

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation
h(t) = -16t² +128t
When will the object reach its maximum height?

a)

4 ft

b)

0 seconds

c)

0 ft

d)

4 seconds

149.

Rafael drops a ball from a third-story window. This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.
h = -5t² + 45
When is the ball at ground level?

a)

only at t = 0 seconds

b)

only at t = 3 seconds

c)

only at t = 9 seconds

d)

at both t = 0 seconds and t = 3 seconds

150.

What word means all of the x-values in a function?

a)

Domain

b)

Range

c)

Integer

d)

Difference

151.

Name the x-intercept(s)?

a)

(0, 0)

b)

(2, 4)

c)

(0, 0) and (0, 4)

d)

(0, 0) and (4, 0)

152.

What are the zeros of the function

f(x)= -4(x - 3)(x+5)?

*Hint: Type the function into y=

a)

(-12,0) and (20,0)

b)

(-5,0) and (3,0)

c)

(-4,0) and (-5,0)

d)

(-3,0) and (5,0)

153.

Which graph has the x intercepts of (-2,0) and (1,0)?

a)

y = 2x -1

b)

y = x²-2x +1

c)

y = x²+x-2

d)

y=x²-x-2

154.

What are the zeros for the function
f(x) = (x + 7)(x + 5)

a)

(7 , 0) and (5 , 0)

b)

(0 , 7) and (0 , 5)

c)

(-7 , 0) and (-5 , 0)

d)

(7 , 0) and (5 , 0)

155.

Write an equation of this graph in intercept (factored) form.

a)

h(x) = (x - 1)(x + 3)

b)

h(x) = (x + 1)(x - 3)

156.

What is the vertex?

a)

(4,-4)

b)

(2,0)

c)

(0,2)

d)

(6,0)

157.

What is the quadratic function for the graph in intercept form?

a)

y = (x - 2)(x - 6)

b)

y = - (x - 2)(x - 6)

c)

y = (x + 2)(x + 6)

d)

y = (x + 4)(x - 4)

158.

The vertex of this quadratic is...

a)

(1,16)

b)

(-3,0)

c)

(5,0)

d)

(0,15)

159.

The point (4, -3) is a...

a)

Maximum

b)

Minimum

160.

How many x-intercepts does this quadratic have?

a)

0

b)

1

c)

2

d)

infinitely many

161.

The curved graph of a quadratic (the U shape)

a)

Quadratic

b)

Parabola

c)

Vertex

d)

Minimum

162.

5(a + 6)

a)

5a + 6

b)

a + 30

c)

5a + 30

163.

-4(2a + 7) + 3a

a)

-5a - 28

b)

11a + 46

c)

5a + 46

164.

(7y + 4)(8y + 2)

a)

58y² + 48y + 6

b)

65y² + 64y + 8

c)

56y² + 46y + 8

d)

56y⁸ + 46y - 8

165.

(2s + 9)(3s - 4)

a)

3s² + 19s - 36

b)

4s² + 19s - 36

c)

5s² + 19s - 36

d)

6s² + 19s - 36

166.

Multiply.
(x + 7)²

a)

x²+ 7x + 7x + 49

b)

x²+ 7x + 7

c)

7x²+ x + 7

d)

x² + 14x + 49

167.

Find the product:
(x−5)²

a)

x² +10x+25

b)

x² − 25

c)

x² −10x+25

d)

x² +25

168.

Multiply:
(3a + 4)²

a)

6a²+12a+16

b)

9a²+24a+16

c)

9a²+12a+16

d)

9a²+16

169.

Always, Sometimes, or Never:
The product of two binomials is a trinomial.

a)

Always

b)

Sometimes

c)

Never

170.

(x - 1)(x - 8)

a)

x² + 9x + 8

b)

x²+ 9x - 8

c)

x² - 9x - 8

d)

x² - 9x + 8

171.

Use FOIL to solve: (p + 9)(4p + 2)

a)

9p x 4p + 2

b)

p to the 5th power minus seven

c)

-18p

d)

4p² + 38p + 18

172.

Which two expressions represent the large rectangle's total area?

a)

5(b + 3)

b)

5b + 3

c)

5b + 15

d)

5(3b)

173.

$\cdot$ Which expression shows the total area as a product of the length and width?

a)

3 $\cdot$ x + 7

b)

3x + 7

c)

3x + 21

d)

3

174.

What numbers represent the two blank spaces of the length of the rectangle?

a)

x and 8

b)

x and 3

c)

x and 12

d)

12x and 12x

175.

What is the missing number in the following area model?

a)

225

b)

545

c)

50

d)

9

176.

Which of the following is the best definition of REVENUE?

a)

The total amount of income a business makes from selling products or services

b)

The amount of money a business has LEFT over after paying for their costs.

c)

The total amount of money a business spends.

d)

The amount of money a business loses every month.

Algebra Semester 2 Final Review

Total questions: 176

Worksheet time: 3hrs 56mins

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