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Graded Activity
Unit Activity: Quadratic Relationships
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Restaurant Revenue
In this activity, you will create quadratic inequalities in one variable and use them to solve problems. Read this scenario,
and then use the information to answer the questions that follow.
Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose the buffet
as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost
of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner
wants the buffet to maintain a minimum revenue of $130 per hour.
Noah wants to model this situation with an inequality and use the model to help him make the best pricing decisions.
Part A
Question
Write two expressions for this situation, one representing the cost per customer and the other representing the
average number of customers. Assume that x represents the number of $1 increases in the cost of the buffet.
Enter the correct answer in the box. Type the cost expression on the first line and the customer expression on the
second line.
Cost:
Customers:
Part B
Question
To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and
the average number of customers per hour. Create an inequality in standard form that represents the restaurant
owner’s desired revenue.
Type the correct answer in each box. Use numerals instead of words.
x2 +
x+
≥
Part C
Question
Which possible buffet prices could Noah could charge and still maintain the restaurant owner’s revenue
requirements?
Select the correct prices in the table.
$12
$13
$14
$15
Part D
Assuming that any increase occurs in whole dollar amounts, what is the maximum possible increase that maintains
the desired minimum revenue? Explain why this is true.
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Graded Activity
Unit Activity: Solving Quadratic Equations
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Methods of Solving Quadratic Equations
In this activity, you will choose a problem-solving method and use it to find the solutions to quadratic equations.
Question 1
Part A
Question
Type the correct answer in each box. Write your answers in decimal form, rounded to the nearest tenth, if
necessary. Type the solution with the smaller value in the first blank.
(Hint: to complete your calculations, you may need to use mental math.)
Select and use the most direct method to solve 2x(x + 1.5) = -1.
x=
or x =
Part B
Question
Type the correct answer in the box.
Solve this equation using the most direct method:
3x(x + 6) = -10
Enter your solution in the exact, most simplified form. If there are two solutions, write the answer using the ±
symbol.
Part C
Describe and justify the methods you used to solve the quadratic equations in parts A and B.
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Question 2
Ann works for a city’s parks and recreation department. She is looking for some commercial land to rezone for
recreational use and has found two possible options.
Part A
Ann’s first option is a plot of land adjacent to a current park. The current park is a square, and the addition will
increase the width by 200 meters to give the expanded park a total area of 166,400 square meters. This equation
represents the area of the first option, where x is the side length of the current square park:
x2 + 200x = 166,400.
Use the most direct method to solve this equation and find the side length of the current square park. Explain your
reasoning for both the solving process and the solution.
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Part B
Ann’s second option is rezoning two separate plots of land. One is square, and the other is triangular with an area
of 32,500 square meters. For this second option, the total area would be 76,600 square meters, which can be
represented by this equation, where x is the side length of the square park:
x2 + 32,500 = 76,600.
Use the most direct method to solve this equation and find the side length of the square-shaped park. Explain your
reasoning for both the solving process and the solution.
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Graded Activity
Course Activity: Writing Exponential Functions
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Exponential Growth and Decay
In this activity, you will use graphs, tables, sets of points, and verbal descriptions to write exponential functions in
mathematical and real-world contexts.
Question 1
Part A
Question
A media company wants to track the results of its new marketing plan, so the video production manager recorded
the number of views for one of the company’s online videos. The results of the first 5 weeks are shown in this
table.
Weeks, x
Views, f(x)
0
5,120
1
6,400
2
8,000
3
10,000
4
12,500
5
15,625
Write an equation to model the relationship between the number of weeks, x, and the number of views, f(x).
Enter the correct answer in the box by replacing the values of a and b.
f !x” = a !b”
x
Part B
Question
During this same time, the digital print manager tracked the number of visits to the website’s homepage. He found
that before launching the new marketing plan, there were 4,800 visits. Over the course of the next 5 weeks, the
number of site visits increased by a factor of 1.5 each week.
Write an equation to model the relationship between the number of weeks, x, and the number of site visits, f(x).
Enter the correct answer in the box by replacing the values of a and b.
f !x” = a !b”
x
Part C
Question
During their team meeting, both managers shared their findings. Complete the statement describing their
combined results.
Select the correct answer from each drop-down menu.
The initial number of video views was
video views grew by
the initial number of site visits, and the number of
the number of site visits.
The difference between the total number of site visits and the video views after 5 weeks is
.
Question 2
Part A
Question
An industrial copy machine has the ability to reduce image dimensions by a certain percentage each time it copies.
A design began with a length of 16 inches, represented by the point (0,16). After going through the copy machine
once, the length is 12, represented by the point (1,12).
Enter the correct answer in the box by replacing the values of a and b.
f !x” = a !b” x
Part B
Question
Another copy machine also has the ability to reduce image dimensions, but by a different percentage. This graph
shows the results found when copying a design x times. Use the graph to write the equation modeling this
relationship.
Enter the correct answer in the box by replacing the values of a and b.
f !x” = a !b”
x
Part C
Question
Both copy machines reduce the dimensions of images that are run through the machines. Which statement is true
about the results of using these copiers?
As the number of copies increases, the dimensions of the images continue to increase toward, but never
reach, positive infinity.
As the number of copies increases, the dimensions of the images continue to increase until reaching 8.
As the number of copies increases, the dimensions of the images continue to decrease until reaching 0.
As the number of copies increases, the dimensions of the images continue to decrease toward, but never
reach, 0.