Module 9: Interpreting Maxima and Minima for Polynomial Functions Quiz

Step 1 of 1

Tight Sealing's most popular product is an electronic high-pressure cooker. Currently, each cookerretails at$50.00, and the company sells approximately40,000cookers annually. The company found that each time the unit price is raised by$5.00, their annual sales decrease by2,000units. If the company raises the unit price by$5.00xtimes, the new price would be50+5x50+5xdollars, and they can sell40,000-2,000x40,000-2,000xcookers annually.

Thisfunction models Tight Sealing's annual revenue, in dollars, from selling the cookers:

f(x)=(50+5x)(40,0002,000x)f(x)=(50+5x)(40,0002,000x).

Examine the following graph representing this function.

[The graph shows a curve that starts at (0, 2,000,000), then rises to (5, 2,250,000) and ends at (20, 0).]

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Question 1 of 11

Question1

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From the function's graph, identify and interpret its minimum.

The function's minimum is0atx=20. This implies the company's minimum revenues from selling the cookers is0. This happens if the unit price is raised20times.

The function's minimum is0atx=20. This implies the company's minimum revenues from selling the cookers is0. This happens if the unit price becomes$20.00.

The function's minimum is2,000,000atx=0. This implies the company's minimum revenues from selling the cookers is2,000,000. This happens if the unit price remains to be$5.00.

The function's minimum is0atx=20. This implies the company's minimum revenues from selling the cookers is$20.00. This happens if the unit price decreases to0.

A company allocated funds for an advertisement campaign. The amount of money in the account as time passes can be modeled by a function,asshown in the following graph.

[A graph plots Days on the horizontal axis and Money in Account in Thousands of Dollars on the vertical axis. A line passes through (0, 160) and (24, 0).] 2018 WGU, Powered by GeoGebra

Question 2 of 11

Question2

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Identify the function'sminimum.

The function's minimum is0atx= 160.

The function's minimum is24atx= 0.

The function's minimum is0atx= 24.

The function's minimum is160atx= 0.

Johan is observing some suspicious activities on aweb server.The followinggraph shows theweb server's CPU usage in the past10minutes.

[The graph shows a curve that starts at (0, 21), then falls to (4, 5), and then ends at (10, 41).]

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Question 3 of 11

Question3

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Identify the function's minimum.

The function's minimum is10.4atx=1.4.

The function's minimum is5atx=4.

The function's minimum is2.5atx=4.

The function's minimum is4atx=5.

Awebserver'snumber of hits since 8:00 a.m. every day can be modeled by the following function.

[The graph shows a curve which starts at a point (0, 10), then passes through the points (1.2, 3), (4.2, 11), (7, 5) and ends at (8, 10).] 2018 WGU, Powered by GeoGebra

Question 4 of 11

Question4

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Identify itsmaximumand interpret its meaning in this context.

The function's maximum is approximately10.5atx= 4.25. It implies theweb serverhas a maximum hit request of10,500, which happens at 12:15 p.m.

The function's maximum is approximately10.9atx= 4.25. It implies theweb serverhas a maximum hit request of10,900, which happens at 12:10 p.m.

The function's maximum is approximately10.9atx= 4.25. It implies theweb serverhas a maximum hit request of10,900, which happens at 12:15 p.m.

The function'smaximum is approximately10.9atx= 4.15. It implies theweb serverhas a maximum hit request of10,900, which happens at 12:09 p.m.

Johan ran some maintenance programs on a server.The followinggraph models available RAM on the server from the moment those programs started runninguntilthe moment they completedrunning.

[The graph shows a curve that starts at (0, 21), then falls to (4, 5), and then ends at (10, 41).]

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Question 5 of 11

Question5

This is not a form; we suggest that you use the browse mode and read all parts of the question carefully.

Identify and interpret the function's maximum.

The function's maximum is24atx=0andx=8.9. It implies the server had maximum available RAM, 24%, when the programs started running and then again when the programs stopped running 8.9 minutes later.

The function's maximum is24atx=0andx=8.8. It implies the server had maximum available RAM, 24%, when the programs started running and then again when the programs stopped running 8.8 minutes later.

The function's maximum is24only atx=0. It implies the server had maximum available RAM, 24%, when the programs started.

The function's maximum is24only atx=8.8. It implies the server had maximum available RAM, 24%,whenthe programs stopped running.

The followingfunction models Winter Gears' sales in the past year.

[The graph shows a curve that starts (0, 9.6), then passes through the points (1.4, 10.4), (9.5, 3.4), and ends at (12, 6).]

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Question 6 of 11

Question6

This is not a form; we suggest that you use the browse mode and read all parts of the question carefully.

Identify the function's minimum.

The function's minimum is10.4atx=1.4.

The function's minimum is9.5atx=3.4.

The function's minimum is3.4atx=9.5.

The function's minimum is3.2atx=9.25.

Harryruns a firework business, and needs to calculate how high fireworks fly. Hefiresafirework into the air on a hill100feet above sea level. The height of the firework's trajectorycan be modeled by the polynomial function in the following graph.

[A graph plots Time in Seconds on the horizontal axis and Height in Feet on the vertical axis. A curve starts at (0, 100), rises to (1.7, 147) and ends at (4.75, 0)] 2018 WGU, Powered by GeoGebra

Question 7 of 11

Question7

This is not a form; we suggest that you use the browse mode and read all parts of the question carefully.

Identify and interpret the function's maximum.

The function's maximum is1.7atx=147. It implies the firework will reach its maximum height of147feet1.7secondsafter it is fired.

The function's maximum is1.7atx=141. It implies the firework will reach its maximum height of141feet1.7secondsafter it is fired.

The function's maximum is141atx=1.7. It implies the firework will reach its maximum height of141feet1.7secondsafter it is fired.

The function's maximum is147atx=1.7. It implies the firework will reach its maximum height of147feet1.7secondsafter it is fired.

The followingchart recorded a company's stock price change in a certain day.

[The graph shows a curve that starts at (0, 3.2), then passes through the points (2.2, 6.2), (6.2, 4.2) andends at (8, 7.2).]

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Question 8 of 11

Question8

This is not a form; we suggest that you use the browse mode and read all parts of the question carefully.

Locate and interpret the function's minimum.

The function's minimum is5.8atx=4.2. It implies the stock's price hit the minimum of$5.80at 12:12p.m.

The function's minimum is3.2atx=0. It implies the stock's price hit the minimum of$8.00at 0:00a.m.

The function's minimum is3.2atx=0. It implies the stock had the minimum price of$3.20at 8:00a.m.

The function's minimum is4.2atx=5.8. It implies the stock's price hit the minimum of$4.20at 1:48p.m.

Tight Sealing's most popular product is an electric high-pressure cooker. Currently, each cookerretailsat$50.00, and the company sells approximately40,000cookers annually. The company found that each time the unit price is raised by$5.00, their annual sales decrease by2,000units. If the company raises the unit price by$5.00xtimes, the new price would be50+5x50+5xdollars, and they can sell40,0002,000x40,0002,000xcookers annually.Thisfunction models Tight Sealing's annual revenue, in dollars, from selling the cookers:

f(x)=(50+5x)(40,0002,000x)f(x)=(50+5x)(40,0002,000x). Examine the following graph representing this function.

[The graph shows a curve that starts at (0, 2,000,000), then rises to (5, 2,250,000) and ends at (20, 0).]

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Question 9 of 11

Question9

This is not a form; we suggest that you use the browse mode and read all parts of the question carefully.

From the function's graph, identify and interpret its maximum.

The function's maximum is2,250,000atx=5. This implies the company's maximum annual revenues from selling the cookers will be$2,250,000. This happens if the company raises the unit price by$5.00five times, making the unit price50+25=7550+25=75dollars.

The function's maximum is2,250,000atx=5. This implies the company's maximum annual revenues from selling the cookers will be$2,250,000. This happens if the company makes the unit price $5.00.

The function's maximum is2,250,000atx=5. This implies the company's maximum annual revenues from selling the cookers will be$2,250,000. This happens if the company raises the unit price by$5.00, making the unit price55dollars.

The function's maximum is2,385,000atx=5. This implies the company's maximum annual revenues from selling the cookers will be$2,300,000. This happens if the company raises the unit price by$5.00five times.

Johan ran some maintenance programs on a server. The following graph models available RAM on the server from the moment those programs started runninguntilthe moment they completed running.

[A graph plots Minutes on the horizontal axis and Available RAM on the vertical axis shows a curve which starts at a point (0, 24), then falls to (4.4, 4.8), and ends at (8.8, 24).] 2018 WGU, Powered by GeoGebra

Question 10 of 11

Question10

This is not a form; we suggest that you use the browse mode and read all parts of the question carefully.

Identify and interpret the function's minimum.

The function's minimum is4.4atx=5.8. It implies the server had the least amount of available RAM,4.4%, 5.8 minutes since the programs started running.

The function's minimum is4.8atx=4.4. It implies the server had the least amount of available RAM,4.8%, 4.4 minutes since the programs started running.

The function's minimum is4.4atx=5.8. It implies the server had the least amount of available RAM, 5.8%, 4.4 minutes since the programs started running.

The function's minimum is4.8atx=4.4. It implies the server had the least amount of available RAM,4.4%, 4.8 minutes since the programs started running.

Krisis designing a video game and needs to model the trajectory of a golf ball.Thisfunction models a golf ball's height, in feet, as a function of the ball's horizontal distance since being hit, in feet.

[The graph shows a downward opening parabola which starts at a point (0, 0) and ends at (57.9, 0) with a maximum at (28.5, 66).] 2018 WGU, Powered by GeoGebra

Question 11 of 11

Question11

This is not a form; we suggest that you use the browse mode and read all parts of the question carefully.

Identify and interpret the function's minimum.

The function has a minimum of0at two places:x=0andx=57.9. The point(0,0)represents the golf ball's starting position before it was hit. The point(57.9,0)implies the golf ball traveled a horizontal distance of57.9feet before hitting the ground.

The function has a minimum of0at one place:x=57.5. It implies the golf ball traveled a horizontal distance of57.5feet before hitting the ground.

The function has a minimum of0at two places:x=0andx=57.5. The point(0,0)represents the golf ball's starting position before it was hit. The point(57.5,0)implies the golf ball traveled a horizontal distance of57.5feet before hitting the ground.

The function has a minimum of0at one place:x=0. It represents the golf ball's starting position, before it was hit.

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