Free Printable Unit 3 and 4 Practice

1.

What is the vertex?
y = -2x² + 4x + 3

a)

(0, 3)

b)

(-1, 5)

c)

(1, 5)

d)

(1, -5)

2.

What is the vertex?
f(x) = 2(x - 5)² + 12

a)

(-5, -12)

b)

(5,-12)

c)

(5, 12)

d)

(-5, 12)

3.

What is the axis of symmetry?
f(x) = x²- 8x + 15.

a)

x = -4

b)

x = 4

c)

y = 4

d)

y = -4

4.

What is the axis of symmetry?
y = 3x²- 6x + 4

a)

x=1

b)

x=-6

c)

x=2

d)

x=-1

5.

What is the vertex?
f(x) = -x²- 4x + 12.

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

6.

What is the vertex?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

7.

What do we call the highest or lowest point of a quadratic?

a)

parabola

b)

vertex

c)

graph

d)

point

8.

How many zeros does this parabola have?

a)

3

b)

2

c)

0

d)

1

9.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

10.

What is the y-intercept?
f(x) = 2(x - 5)² + 12

a)

(0, -5)

b)

(0,12)

c)

(0, 62)

d)

(0, 212)

11.

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

a)

(0, 6)

b)

(0, -6)

c)

(6, 0)

d)

(-6, 0)

12.

What is the standard form formula?

a)

y=mx+b

b)

y=ax²+bx+c

c)

y=a(x-h)2+k

13.

What is the vertex form formula?

a)

y=ax²+bx+c

b)

y=mx+b

c)

y=a(x-h)2+k

14.

Is the graph shown above a max or min?

a)

Maximum

b)

Minimum

15.

What is the domain of the graph shown above.

a)

x=19

b)

all real numbers

c)

y=3

d)

Maximum

16.

What are the zeros of the graph shown above?

a)

2 and 6

b)

4 and 2

c)

6 and 9

d)

5 and 1

17.

What is a axis of symmetry?

a)

all real numbers

b)

y=5

c)

the line that divides the graph in equal halves

d)

y=mx+b

18.

Is the graph shown above a max or min?

a)

Minimum

b)

Maximum

19.

What is the y-intercept of the graph shown above?

a)

all real numbers

b)

(0,6)

c)

(0,2)

d)

(0,-6)

20.

What is the vertex of the graph shown above?

a)

(7,6)

b)

(-1,2)

c)

(2,-1)

d)

(5,0)

21.

Graph the following equation:

y=x²-2x-3

a)

b)

c)

d)

22.

What does the h term tell you?

a)

left or right

b)

left or right, opposite sign, axis of symmetry, x-value of the vertex.

c)

axis of symmetry, x-value of the vertex

d)

nothing.

23.

What does the k term tell you?

a)

up.

b)

down.

c)

up/down, y-value in the vertex

d)

nothing

24.

Describe the transformations below: $\left(x+1\right)^2-4$

a)

left: 1, up: 4

b)

left: 1, down: 4

c)

right: 1, up: 4

d)

right: 4, up: 1

25.

Describe the transformation below: $-\left(x+3\right)^2+6$

a)

reflect over the x-axis

b)

reflect over the x-axis, left: 3, up: 6

c)

stretch, left: 3, down: 6

d)

left: 3, down: 6

26.

Describe the transformation below: $-3\left(x+4\right)^2-1$

a)

stretch by 3, right: 4, down: 1

b)

reflect over the x-axis, right: 4, down: 1

c)

reflect over the x-axis, stretch by 3, left: 4, down: 1

d)

stretch by 4, down: 3, left: 1

27.

Identify the a, h, and k term from the following equation: $\left(x+3\right)^2+2$

a)

a=-1, h=3, k=2

b)

a=3, h=3, k=3

c)

a=1, h=-3, k=2

d)

a=1, h=-3, k=-2

28.

Identify the a, h, and k terms in the following equation: $2\left(x+4\right)^2-1$

a)

a=2, h=-4, k=-1

b)

a=-2, h=4, k=1

c)

a=2, h=4, k=1

d)

a=-2, h=-4, k=1

29.

Identify the a, h, and k terms in the following equation: $\left(x+4\right)^2-3$

a)

a=-1, h=4, k=3

b)

a=-1, h=-4, k=3

c)

a=1, h=4, k=3

d)

a=1, h=-4, k=-3

30.

Determine the vertex from the following equation: $-3\left(x-4\right)^2+1$

a)

Vertex: (4,1)

b)

Vertex: (-4, -1)

c)

Vertex: (4, -1)

d)

Vertex: (-4, 1)

31.

Determine the vertex from the following equation: $-\left(x+1\right)^2-1$

a)

Vertex: (1,-1)

b)

Vertex: (-1, 1)

c)

Vertex: (-1, -1)

d)

Vertex: (1, 1)

32.

Determine the vertex from the following equation: $\frac{1}{2}\left(x+4\right)^2+1$

a)

Vertex: (-4, 1)

b)

Vertex: (-4, -1)

c)

Vertex: (4, 1)

d)

Vertex: (4, -1)

33.

Determine the axis of symmetry from the following equation: $-\left(x-2\right)^2+4$

a)

A. O. S: 2

b)

A. O. S: 4

c)

A. O. S: -2

d)

A. O. S: -1

34.

Determine the axis of symmetry of the following equation: $-2\left(x+2\right)^2+3$

a)

A. O. S: 3

b)

A. O. S: -2

c)

A. O. S: 2

d)

A. O. S: 1

35.

Determine if the parabola has a maximum or minimum, if it opens up (+) then it will have a minimum, if it opens down (-) then it will have a maximum. $3\left(x+3\right)^2-2$

a)

Maximum

b)

Minimum

36.

Determine if the following equation has a maximum or minimum: $-\left(x-2\right)^2+7$

a)

Maximum

b)

Minimum

37.

Determine if the following function will be narrow (stretch) or wider (shrink): $4\left(x-3\right)^2+4$

a)

Narrow

b)

Wider

38.

Determine if the following is narrow or wider: $\frac{2}{3}\left(x+3\right)^2+6$

a)

Narrow

b)

Wider

39.

What is a quadratic funtion in the form of $f\left(x\right)=a\left(x-h\right)^2+k$ called?

a)

Factored Form

b)

Standard Form

c)

Vertex Form

40.

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

41.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

42.

What should you do first in solving this equation?

x² + 6x - 13 = 3

a)

Factor

b)

Write down: a = 1, b = 6, c = -13

c)

Subtract 3 from both sides.

d)

Add 3 to both sides.

43.

Solve using the quadratic formula.
2x² - 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

44.

2x²-x -3=0

a)

x=-3/2 x=1

b)

x= 3/2 x= -1

c)

x= -3/2 x= -1

d)

x= 3/2 x= 1

45.

$2m^2=-2m+12$
Solve using the quadratic formula.

a)

$x=2,-3$

b)

$x=3,-2$

c)

$x=1\pm\sqrt{13}$

d)

No Solution

46.

Solve using the quadratic formula...

9x² = 4 + 7x

a)

b)

c)

d)

No solution

47.

What is the "c" value in the equation..

4x^2=18

a)

4

b)

18

c)

0

d)

-18

48.

$w^2+7w+4=0$

a)

$\frac{-7\pm\sqrt{33}}{2}$

b)

$\frac{-7\pm\sqrt{65}}{2}$

c)

$\frac{7\pm\sqrt{33}}{2}$

d)

$\frac{-7\pm3\sqrt{11}}{2}$

49.

$5x^2+3x-3=0$

a)

$\frac{-3\pm i\sqrt{51}}{10}$

b)

$\frac{-3\pm\sqrt{69}}{10}$

c)

$\frac{3\pm\sqrt{69}}{2}$

d)

$\frac{-3\pm3\sqrt{23}}{10}$

50.

Is the pictured graph growth, decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

51.

Which of the following functions shows an initial amount of $15 and an decrease of 35% each year?

a)

y = 15(0.35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.65)^x

d)

y = 35(20)^x

52.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

53.

How many times a year is annually?

a)

1

b)

4

c)

52

d)

365

54.

Emily’s parents put $1,500 in her bank account for college tuition. At an interest rate of 8.25% compounded semiannually,what will be the balance after 18 years? (round to the nearest cent)

a)

$6,273.50

b)

$6,314.08

c)

$6,385.72

d)

$6,427.94

55.

The Henley's took out a loan for $195,000 to purchase a home. At a 4.3% interest rate compounded annually, what will be the balance after 30 years? (round to the nearest cent)

a)

$412,749.79

b)

$429,305.61

c)

$689,547.00

d)

$689,546.99

56.

Elise has $100 in her bank account. The account earns 2% interest every year. Which function would you use for this situation?

a)

f(x) = a(b)^x

b)

f(x) = a(1-r)^x

c)

f(x) = a(1+r)^x

d)

f(x) = a(b)^(x-h) + k

57.

Jane has 3 bunnies in her back yard. Each day, the bunny population triples. Which function would you use for this situation?

a)

f(x) = a(b)^x

b)

f(x) = a(1-r)^x

c)

f(x) = a(1+r)^x

d)

f(x) = a(b)^(x-h) + k

58.

Jacob bought a Dodge Charger. Each year, the value of the car depreciates by 10%. Which function would you use for this situation?

a)

f(x) = a(b)^x

b)

f(x) = a(1-r)^x

c)

f(x) = a(1+r)^x

d)

f(x) = a(b)^(x-h) + k

59.

Given the function
f(x) = 1(3)^(x-2)+7
Which number represents a HORIZONTAL translation?

a)

1

b)

3

c)

2

d)

7

60.

Given the function
f(x) = 1(3)^(x-2)+7
Which number represents a VERTICAL translation?

a)

1

b)

3

c)

2

d)

7

61.

Given the function
f(x) = 1(4)^(x-6)+10
What is the horizontal translation?

a)

The graph moves right 10 units.

b)

The graph moves right 6 units.

c)

The graph moves left 6 units.

d)

The graph moves right 4 units.

62.

Given the function
f(x) = 1(4)^(x-6)+10
What is the vertical translation?

a)

The graph moves up 10 units.

b)

The graph moves down 6 units.

c)

The graph moves 1 unit up.

d)

The graph moves up 4 units.

63.

The following function represents a bank account.
g(x) = 200(1.25)^x
What was the initial dollar amount put in the bank?

a)

$200

b)

$1.25

c)

$0.25

d)

$2.00

64.

The following function represents a bank account.
g(x) = 200(1.25)^x
What is the common ratio?

a)

200

b)

1.25

c)

0.25

d)

2.00

65.

The following function represents a bank account.
g(x) = 200(1.25)^x
What is the rate the bank is paying?
*Remember the rate is added or subtracted to 1 inside parenthesis*

a)

200%

b)

1.25%

c)

25%

d)

2%

66.

Ty's house is worth $100,000 right now. It will lose value at a rate of 2% per year.
Which function models this situation?

a)

f(x) = 100,000(2)^x

b)

f(x) = 100,000(1.02)^x

c)

f(x) = 100,000(0.98)^x

d)

f(x)=100,000(98)^x

67.

The function g(x) = 120(0.88)^xRepresents the number of pets at a pet store.
Which statement is true about this function?

a)

Twelve percent of pets get adopted every day.

b)

Eighty eight percent of pets get adopted every day.

c)

The pet store started with eighty eight pets.

d)

One hundred twenty pets are adopted every day.

68.

What type of function is f(x)=2(1/7)^x ?

a)

quadratic

b)

Linear

c)

Exponential

69.

How many times a year is quarterly?

a)

1

b)

4

c)

52

d)

365

70.

This is an example of:

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

71.

This is an example of:

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

72.

This is an example of:

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

73.

This is an example of:

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

74.

This is an example of: $f\left(x\right)=\ 25\ \left(\ 0.20\right)^x$

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

75.

How do you know that this was exponential decay? $f\left(x\right)=\ 25\ \left(\ 0.20\right)^x$

a)

Because the 25 was bigger than one

b)

Because the 0.20 was bigger than one

c)

Because the 25 was less than one

d)

Because the 0.20 was less than one

76.

This is an example of: $f\left(x\right)=\ 0.25\ \left(\ 1.3\right)^x$

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

77.

How do you know that this was exponential growth? $f\left(x\right)=0\ .25\ \left(\ 1.3\right)^x$

a)

Because the 0.25 was bigger than one

b)

Because the 1.3 was bigger than one

c)

Because the 0.25 was less than one

d)

Because the 1.3 was less than one

78.

This is an example of: $f\left(x\right)=90\ \left(\ \frac{1}{2}\right)^x$

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

79.

How do you know that this was exponential decay? $f\left(x\right)=90\ \left(\ \frac{1}{2}\right)^x$

a)

Because the 90 was bigger than one

b)

Because the 1/2 was bigger than one

c)

Because the 90 was less than one

d)

Because the 1/2 was less than one

80.

This is an example of: $f\left(x\right)=3\ \left(\ \frac{5}{2}\right)^x$

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

81.

How do you know that this was exponential growth? $f\left(x\right)=3\ \left(\ \frac{5}{2}\right)^x$

a)

Because the 3 was bigger than one

b)

Because the 5/2 was bigger than one

c)

Because the 3 was less than one

d)

Because the 5/2 was less than one

82.

This function represents the number of ants in a colony $f\left(x\right)=3\ \left(\ 2\right)^x$ How many ants did you begin with?

a)

There was 2 ants

b)

There was 3 ants

c)

The equation doesn't tell us

83.

This function represents the number of ants in a colony $f\left(x\right)=3\ \left(\ 2\right)^x$ What is the growth rate?

a)

The ants are growing by 3 times

b)

The ants are growing by 2 times

c)

The equation doesn't tell us

84.

How do we know that is an example of an exponential growth?

a)

Its a line going up

b)

Its a line going down

c)

Its a smooth curve going down

d)

Its a smooth curve going up

85.

How do we know that is an example of an exponential decay?

a)

Its a line going up

b)

Its a line going down

c)

Its a smooth curve going down

d)

Its a smooth curve going up

86.

What is the equation of the horizontal asymptote for following exponential function?

a)

y = -4

b)

y > -4

c)

y < -4

d)

(0, -3)

87.

What is the equation of the horizontal asymptote for following exponential function?

a)

y = -2

b)

y > -2

c)

y < -2

d)

(0, -2)

88.

What is the equation of the horizontal asymptote for following exponential function?

a)

y = 1

b)

y = 2

c)

y > 1

d)

(0, 2)

89.

What is the equation of the horizontal asymptote for following exponential function?

a)

y = 6

b)

y = 5

c)

y < 5

d)

(0, 5)

90.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

91.

What type of function is

$f\left(x\right)=\left(\frac{1}{7}\right)^x$

a)

Exponential Growth

b)

Linear

c)

Exponential Decay

92.

The horizontal line that a exponential function approaches but never touches

a)

Asymptote

b)

Growth Factor

c)

Axis of Symmetry

93.

What is the asymptote of the parent function y=2^x?

a)

x=0

b)

y=0

c)

x=2

d)

y=2

94.

What is the range of f(x) = 5^x?

a)

-∞ ≤ x ≤ ∞

b)

-∞ ≤ y ≤ ∞

c)

x > 0

d)

y > 0

95.

What is the domain of f(x) = 5^x?

a)

-∞ ≤ x ≤ ∞

b)

-∞ ≤ y ≤ ∞

c)

x > 0

d)

y > 0

96.

What is the Domain of this exponential function?

a)

y=1

b)

x=0

c)

All Real Numbers

d)

x>0

97.

What is the Range of this function?

a)

y> 0

b)

x> 0

c)

All Real Numbers

d)

y= 1

98.

What is the Domain of this exponential function?

a)

y > 0

b)

y < 0

c)

All Real Numbers

d)

y > 0

99.

What is the range of the exponential function?

a)

all real numbers

b)

y > -1

c)

y < -1

d)

x > -1

100.

What is the range of the exponential function?

a)

all real numbers

b)

y > -3

c)

y < -3

d)

x > -3

101.

What is the Range of the exponential?

a)

y > -8

b)

y ≥ -8

c)

All real numbers

d)

y < -8

102.

Name the asymptote.

a)

x = -4

b)

y = -5

c)

y = -4

d)

x = -5

103.

Name the range.

a)

All Real Numbers

b)

y > -5

c)

y ≥ -5

d)

y < -5

104.

Name the domain.

a)

x> -4

b)

y > -5

c)

y < -4

d)

all real numbers

105.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

106.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

107.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the decay factor?

a)

^.08

b)

^1.08

c)

.92

d)

8

108.

A collectible car has been going up in price by 10% each year. If the car is already worth $29,000, how much will the car be worth in 5 years?

a)

$0.29

b)

$2,900,000,000

c)

$46,704.79

d)

$145,000

109.

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
Is the population of elephants increasing or decreasing?

a)

Increasing

b)

Decreasing

110.

The value of a car purchased for $20,000 decreases at a rate of 12% per year. What will be the value of the car after 3 years?

a)

$12,800.00

b)

$13,629.44

c)

$17,600.00

d)

$28,098.56

111.

The amount of ibuprofen (medicine for headaches) breaks down by 30% each hour. If a person took a 200 milligram ibuprofen, how much will be left after 3 hours?

a)

5.4 mg

b)

68.6 mg

c)

.0054 mg

d)

2,400,000 mg

112.

Find the balance in an account that has $300 invested at 6.5% for 4 years compounded semi-annually.

a)

$387.47

b)

$496.50

c)

$7,800.00

d)

$385.94

113.

Katy deposited $90 in a savings account earning 5% interest, compounded quarterly. Which of the following equations could represent the amount of money in her account yearly?

a)

b)

c)

d)

114.

Does the following equation show growth or decay?
y=10,000*(0.76)^x

a)

Growth

b)

Decay

115.

The population of Hickory NC, can be modeled by P=6191(1.04)t where t is the number of years since 1995. What was the population in 1995?

a)

6191

b)

1

c)

1995

d)

1.04

Unit 3 and 4 Practice

Total questions: 115

Worksheet time: 6hrs 45mins

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