Module 6: Interpreting Inputs and Outputs for Polynomial Functions Quiz

Step 1 of 1

The following scatterplot shows Broadband Dish's customer satisfaction rate, in percentage,over the past year (wherex= 1 corresponds to January of last year). Apolynomialcurve of best fit is given with its equation and the correspondingcoefficient of determination.

[The parabola f of x equals 0.3081 x squared minus 4.3128 x plus 83.3414 begins at (0, 83), has a minimum at (7, 68) and ends at (14, 83). A series of data points closely approximate the parabola. Text on the graph reads: r squared equals 0.98.

Question 1 of 15

Question1

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Based on the regression function, predict the company's customer satisfaction rate on January 1 of this year.

The company's customer satisfaction rate on January 1 of thisyear would beapproximately79.2%.

The curve cannot predict data because there is an outlier.

The company's customer satisfaction rate on January 1 of thisyear would beapproximately80%.

The company's customer satisfaction rate on January 1 of the next year would beapproximately82.2%.

Question 2 of 15

Question2

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Ditteruns a business that installs fences. His customer gave him200yards of fence to build a rectangular pen. Ditte was instructed to encompass as much area as possible. Assume the pen's length will bexyards; then the pen's area, in square yards, can be modeled by the function:

A(x)=x2+100xA(x)=x2+100x.

If the pen's length is80yards, what's the pen's area?

If the pen's length is80yards, the pen's area is80square yards.

If the pen's length is80yards, the pen's area is1,600square yards.

If the pen's length is80yards, the pen's area is14,400square yards.

If the pen's length is80yards, the pen's area is640square yards.

Question 3 of 15

Question3

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Traffic over a certain bridge every day, in number of vehicles per minute, can be modeled by the functionn(t)=2t3+40t2200t+350n(t)=2t3+40t2200t+350, wheretis the number of hours since8:00a.m.Find the number ofvehiclesper minutethat crossover the bridge at4:30p.m.every day.

Approximately78vehicles per minute go over the bridge at4:30p.m. every day.

Approximately194vehicles per minute go over the bridge at4:30p.m. every day.

Approximately3,373vehicles per minute go over the bridge at4:30p.m. every day.

Approximately312vehiclesper minutecross overthe bridge at4:30p.m. every day.

The following data show the number of PCs Progress Hospital purchased every year since 2000. A function of best fit is given with the corresponding coefficient of determination.

[The graph plots Years since 2000 on the horizontal axis and Number of P Cs Purchased on the vertical axis. Data points are plotted in the shape of an approximately downward opening parabola that passes through (0, 120) to (15, 280), reaches its maximum at (8, 460). An outlier is plotted at (6, 200). A parabola has a vertex at (9, 410) and passes through (0, 120) and (18, 100). All values approximated. The following text is shown on the graph. F of x equals negative 3.8 x squared plus 67.67 x plus 121.7 and r equals 0.74.

Question 4 of 15

Question4

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Choose the correct statement about this regression function.

If the curve is shifted to the right by a little bit, the bettercoefficient of determinationcan be achieved.

If the curve is shifted down, the bettercoefficient of determinationcan be achieved.

Among all 2nd-degree polynomial functions,f(x)f(x)has the highest coefficient of determination for this dataset.

If the curve is shifted up, the bettercoefficient of determinationcan be achieved.

All Corners and Real Voice are cell phone service providers. Their customer satisfaction rates since 2000 are shown in the followinggraph.

[The graph plots Years since 2000 on the horizontal axis and Customer Satisfaction Rate on Percentage in the vertical axis. It shows two curves labelled Real Voice and All Corners. The curve labelled Real voice begins at (0, 64.5), reaches its minimum at (7, 45), and ends at (15, 70.5). The curve labelled All Corners begins at (0, 74), reaches its minimum at (9, 50), and ends at (15, 61). The two curves intersect at (10.9, 51).

Question 5 of 15

Question5

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What is the difference in their customer satisfaction rates in mid-2013?

In mid-2013, Real Voice's customer satisfaction rate was6%higher than All Corners' rate.

In mid-2013,All Corners' customer satisfaction rate was9%higher than Real Voice's rate.

In mid-2013, All Corners' customer satisfaction rate was6%higher than Real Voice's rate.

In mid-2013,Real Voice's customer satisfaction rate was9%higher than All Corners' rate.

The number of memberships at Sunrise Sky Spa since 2000 can be modeled by the function

m(t)=0.6t420t3+200t2500t+1000m(t)=0.6t420t3+200t2500t+1000,

wheretis the number of years since 2000.

[The graph plots Years since 2000 on the horizontal axis and Number of Memberships on the vertical axis. A curve falls from the second quadrant through (0, 1000) to (1.6, 600), and the rises to (9, 2050). From there, it falls to (14.6, 1350) and then rises through (19, 4500).

Question 6 of 15

Question6

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Estimate the solutionor solutionsfor theequationm(t)=2000m(t)=2000.

t7.8,t10t7.8,t10

t7.8,t10,t16.8t7.8,t10,t16.8

t7.9,t10,t16t7.9,t10,t16

t7.95,t10,t17.6t7.95,t10,t17.6

The number of memberships at Sunrise Sky Spa since 2000 can be modeled by the function

m(t)=0.6t420t3+200t2500t+1000m(t)=0.6t420t3+200t2500t+1000,

wheretis the number of years since 2000.

[The graph plots Years since 2000 on the horizontal axis and Number of Memberships on the vertical axis. A curve falls from the second quadrant through (0, 1000) to (1.6, 600), and the rises to (9, 2050). From there, it falls to (14.6, 1350) and then rises through (19, 4500).

Question 7 of 15

Question7

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Estimate the solutionor solutionsfor theequationm(t)=2500m(t)=2500.

t 18.25

t 17.4

t 7.8, t 17.4

t 7.9,t 17.7

Jennifer's Cookies sells well in the Midwest region. Each time the company raises the cookie's priceby$0.05, it sells approximately100fewer bags per day. The following graph shows a scatterplot of the company's income based on how many times it raised per-package priceby$0.05. A curve of best fit is calculated with the corresponding coefficient of determination. In the graph, point Z shows the maximumoff(x)f(x).

[The curve f of x equals negative 10.59 x squared plus 370.92 x plus 32441.45 passes through (0, negative 5) and (35, 33,000) and has a maximum at (17, 35,500) which is labelled: Z equals (17.51, 35,689.16).A series of data points closely follow the parabola and a data point N is plotted well below the parabola at (16, 34,000). Text on the graph reads, r squared equals 0.88]2018 WGU, Powered by GeoGebra

Question 8 of 15

Question8

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Which statement is correct about the outlier?

Point N didnotaffect thecoefficient of determination.

Point N caused the coefficient of determination to be lower than it should be.

Point N caused thecoefficient of determinationto be greater than 1.

Point N caused thecoefficient of determinationto be higher than it should be.

Question 9 of 15

Question9

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Gas is getting more and more expensive.Sheais a student with a tight budget, so she wants the highest fuel efficiency from her car. This function,e(s)e(s), models her car's fuel efficiencyin miles per gallon, depending ons, the car's speed in miles per hour. The function's equation is

e(s)=0.01s2+0.95s+9.1e(s)=0.01s2+0.95s+9.1.

Calculate the car's fuel efficiency when the car's speed is55miles per hour.

The car's fuel efficiency is61.65miles per gallon when the car's speed is55miles per hour.

The car's fuel efficiency is55miles per gallon when the car's speed is61.65miles per hour.

The car's fuel efficiency is31.1miles per gallon when the car's speed is55miles per hour.

The car's fuel efficiency is55miles per gallonwhenthe car's speed is31.1miles per hour.

Question 10 of 15

Question10

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The number of memberships at Sunrise Sky Spa since 2000 can be modeled by the function

m(t)=0.6t420t3+200t2500t+1000m(t)=0.6t420t3+200t2500t+1000,

wheretis the number of years since 2000. Calculate the number of memberships at the beginning of 2008.

There were approximately529memberships at the beginning of 2008.

There were approximately 2,018memberships at the beginning of 2008.

There were approximately 1,024memberships at the beginning of 2008.

There were approximately 2,024memberships at the beginning of 2008.

Question 11 of 15

Question11

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The number of memberships at Sunrise Sky Spa since 2000 can be modeled by the function

m(t)=0.6t420t3+200t2500t+1000m(t)=0.6t420t3+200t2500t+1000,

wheretis the number of years since 2000. Calculate the number of memberships in mid-2002.

There were approximately711memberships in mid-2002.

There were approximately429memberships in mid-2002.

There were approximately 1,928memberships in mid-2002.

There were approximately 3,021memberships in mid-2002.

Jennifer's Cookies sells well in the Midwest region. Each time the company raises the cookie's priceby$0.05, it sells approximately100fewer bags per day. The following graph shows a scatterplot of the company's income based on how many times it raised per-package pricingby$0.05. A curve of best fit is calculated with the corresponding coefficient of determination. In the graph, point Z (arrow) shows the maximumoff(x)f(x).

[The curve f of x equals negative 10.59 x squared plus 370.92 x plus 32441.45 passes through (0, negative 5) and (35, 33,000) and has a maximum at (17, 35,500) which is labelled: Z equals (17.51, 35,689.16).A series of data points closely follow the parabola and a data point N is plotted well below the parabola at (16, 34,000). Text on the graph reads, r squared equals 0.88

Question 12 of 15

Question12

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Which statement is correct about the outlier, point N?

Point N caused point Z to be higher than it should be.

Point N caused point Z to be lower than it should be.

Point N caused point Z to be more to the left than it should be.

Point N didnotaffect point Z's position.

Top Toys released two new toy planes. Plane 1 is simply launched into the air by hand and then falls onto the ground. Plane 2 has a motor and can fly upward. The following graph shows the height of those two planes, in feet, during a test.

[The curve p 1 of t begins at the origin, reaches its maximum at (6, 18), and ends at (12, 0). The curve p 2 of t begins at the origin, passes through the points (2.4, 21.5), (6, 14.8), (9.6, 21.6), and ends at (12, 0). The two curves intersect at (4.5, 17) and (7.4, 17)

Question 13 of 15

Question13

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Estimate the value ofp1(t)p1(t)whent= 7, and interpret its meaning in this context.

The point(7,16.5)implies that Plane 1 was approximately16.5ft. in the air7seconds after it was launched.

The point(7,17.5)implies that Plane 1 was approximately7ft. in the air17.5seconds after it was launched.

The point(7,17.5)implies that Plane 1 was approximately17.5ft. in the air7seconds after it was launched.

The point(7,16.5)implies that Plane 1 was approximately7ft. in the air16.5seconds after it was launched.

Top Toys released two new toy planes. Plane 1 is simply launched by hand into the air and then falls onto the ground. Plane 2 has a motor and can fly upward. The following graph shows theheight of those two planes, in feet, during a test.

[The curve p 1 of t begins at the origin, reaches its maximum at (6, 18), and ends at (12, 0). The curve p 2 of t begins at the origin, passes through the points (2.4, 21.5), (6, 14.8), (9.6, 21.6), and ends at (12, 0). The two curves intersect at (4.5, 17) and (7.4, 17).

Question 14 of 15

Question14

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Estimate the value ofp1(t)p1(t)whent= 7. Writetheanswer in function notation.

(7, 16.5)

(7, 17.5)

p1(7)16.5p1(7)16.5

p1(7)17.5p1(7)17.5

Top Toys released two new toy planes. Plane 1 is simply launched by hand into the air and then falls onto the ground. Plane 2 has a motor and can fly upward. The following graph shows theheight of those two planes, in feet, during a test.

[The curve p 1 of t begins at the origin, reaches its maximum at (6, 18), and ends at (12, 0). The curve p 2 of t begins at the origin, passes through the points (2.4, 21.5), (6, 14.8), (9.6, 21.6), and ends at (12, 0). The two curves intersect at (4.5, 17) and (7.4, 17).

Question 15 of 15

Question15

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Estimate the value ofp2(t)p2(t)whent= 8. Write the answer in function notation.

p2(8)18.1p2(8)18.1

p2(8)18.4p2(8)18.4

Whent= 8,p2(t)p2(t)'s value is approximately 18.1.

(8, 18.4)