Answers26MATH_Recovery_Alg1B22Quadratic Functions: Vertex Form

Analyzing Functional Relationships Answers

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An airline company uses the graph of the function below to display the percent above or below the average price per ticket for a specific route, where x is the price the passenger paid and f(x) is the positive percent difference.

Question illustration
A
The average price per ticket is $250.
B
The minimum price per ticket is $250.
C
The maximum difference paid is 250%.
D
The average difference is 250%.
2
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A fountain sprays water into a pool as part of the filtration system. The projected path of water is modeled by the function given in the table, where x represents the time in seconds since the water left the fountain and f(x) represents the height in feet above the pool’s water line.

Question illustration
A
–6
B
1.5
C
3
D
5
3

A function that models the profit for a new pet-monitoring system shows that there is no profit made until the price reaches $95 per unit, a maximum profit at a price of $140 per unit, and no profit at a price over $185 per unit. Which graph models the function?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
4

A small dairy farm writes a business plan. It includes a graph showing the estimated amount of feed used each day in thousands of pounds, y, compared to the number of years since the farm began operating, x.

Question illustration
A
the estimated amount of years the farm can afford feed
B
the maximum feed per day estimated for the life of the farm
C
the estimated amount of feed per day for the start of the farm
D
the maximum years the farm needs the originally estimated feed per day
5

An investment group compares returns on an account against the function represented in the table, where x is the time in years and f(x) is the total return on investment.

Question illustration
A
a decreasing quadratic function
B
an increasing quadratic function
C
a decreasing exponential function
D
an increasing exponential function
6

The graph models the decay of a sample of iodine-125, where x is the time that has passed and y is the amount remaining in the sample in grams.

Question illustration
A
12.5 grams
B
25 grams
C
50 grams
D
120 grams
7

Consider the graph that represents the path of a golf ball, where x is the distance traveled in feet and f(x) is the height of the ball in yards.

Question illustration
A
The ball traveled a total distance of 50 yards.
B
The ball traveled a total distance of 70 feet.
C
The ball reached a maximum height of 50 feet.
D
The ball reached a maximum height of 70 yards.
8

The computer rendering of a mural in a town’s square uses the function represented in the table to define the outline of a mountain in the town’s logo, where x is the distance in feet from the edge of the mural and f(x) is the distance from the ground in feet.

Question illustration
A
The highest point of the mountain defined by the function is 12 feet.
B
The highest point of the mountain defined by the function is 16 feet.
C
The width of the base of the mountain defined by the function is 12 feet.
D
The width of the base of the mountain defined by the function is 16 feet.
9

A country commits to decreasing spending for infrastructure in various ways at a rate of 30% per year. At the time of the announcement, the country is spending $12 billion per year. Which graph models the amount of infrastructure spending for future years?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
10

A game requires players to throw a ball into a target. The table below shows values from the function that represents one path of a thrown ball, where x represents the horizontal distance the ball travels in feet and f(x) represents the height of the ball in feet.

Question illustration
A
1.5 feet
B
4 feet
C
28 feet
D
29 feet
11

The graph shows the path of light from a wall reflecting off mirrored ceiling tiles, where x is the distance from the wall in feet and y is height in feet along the wall where the light source hangs.

Question illustration
A
The ceiling is 10 feet high.
B
The ceiling is 20 feet high.
C
The light source is 10 feet off the ground.
D
The light source is 20 feet off the ground.
12

In order to set a staff schedule, a fast-food restaurant manager looks at the average rate of customers served per minute during a lunch service. The manager notices that the time period starts with a sharp but steady increase, is followed by a period during which the restaurant is constantly serving the maximum number of customers per minute, and then has a slow but steady decline.

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
13

When planning road development, the road commission estimates the future population using the function represented in the table, where x is the time in years and f(x) is the total population.

Question illustration
A
the maximum population of the city
B
the expected population in 5 years
C
the initial population at the time of the estimation
D
the amount of increase in the population in 5 years
14

The rate of collection by a solar panel decreased steadily throughout the day due to increasing cloud cover until it reached a constant amount. Later in the day, there were two short periods where the Sun appeared, only for the cloud cover to return.Which graph models the amount of energy collected depending on the time since the cloud cover began?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
15

The graph of the function f(x) = (x + 2)(x − 4) is shown.

Question illustration
a
all real values of x where x < −2
a
all real values of x where −2 < x < 4
a
all real values of x where 1 < x < 4
a
all real values of x where x < 0
16

The graph of an exponential function and a linear function are shown below. Exponential Linear Which statement is true about the functions?

Question illustration
T
The exponential function is generally growing slower than the linear function.
T
The exponential function is generally growing faster than the linear function.
T
The linear function is generally growing faster than the exponential function.
T
The exponential function and the linear function are generally growing at the same rate.
17

The function f(x) = –x2 – 4x + 5 is shown on the graph.

Question illustration
T
The domain of the function is all real numbers less than or equal to −2.
T
The domain of the function is all real numbers less than or equal to 9.
T
The range of the function is all real numbers less than or equal to −2.
T
The range of the function is all real numbers less than or equal to 9.
18

The number of rows in an auditorium can be represented by the function f(x) = 80x.The number of seats in each row can be represented by the function g(x) = x + 7.Which function represents the total number of seats, h(x) = f(x)g(x)?

h
h(x) = 136x
h
h(x) = 80x2 + 560x
h
h(x) = 80x + 560
h
h(x) = 80x2 + 560
19

x

e
exponential
l
linear
q
quadratic
s
square root
20

Over which interval does the exponential show a more rapid rate of change?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D

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