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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.