Algebra Module 8

(8.01) A particular company's net sales, in billions, from 2008 to 2018 can be modeled by the expression t2 + 10t + 68, where t is the number of years since the end of 2008. What does the constant term of the expression represent in terms of the context?

• The company earned 68 billion dollars from 2008 to 2018.

• The company earned 68 billion dollars in 2008.

• The company earned 10 billion dollars from 2008 to 2018.

• The company earned 10 billion dollars in 2008.

(8.01) What are the x-intercepts of the parabola?

• (4.5, 0) and (5, 0)

• (0, 4.5) and (0, 5)

• (0, 5) and (0, 4)

• (5, 0) and (4, 0)

(8.01) A soccer ball is kicked toward the goal. The height of the ball is modeled by the function $h(t)=−16t^2+48t$ , where t equals the time in seconds and h(t) represents the height of the ball at time t seconds. What is the axis of symmetry, and what does it represent?

• t = 3; It takes the ball 3 seconds to reach the maximum height and 3 seconds to fall back to the ground.

• t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.

• t = 1.5; It takes the ball 1.5 seconds to reach the maximum height and 3 seconds to fall back to the ground.

• t = 1.5; It takes the ball 1.5 seconds to reach the maximum height and 1.5 seconds to fall back to the ground.

(8.01) A farmer is tracking the amount of corn his land is yielding each year. He finds that the function $f(x)=−x^2+20x+50$ models the crops in pounds per acre over x years. Find and interpret the average rate of change from year 1 to year 10.

• The crop yield increased by 9 pounds per acre from year 1 to year 10.

• The crop yield decreased by 0.09 pounds per acre from year 1 to year 10.

• The crop yield decreased by 11 pounds per acre from year 1 to year 10.

• The crop yield increased by 99 pounds per acre from year 1 to year 10.

(8.01) Finn removes the plug from a trough to drain the water. The volume, in gallons, in the trough after it has been unplugged can be modeled by the expression $12x^2−13x+3$ , where x is the time in minutes. Choose the appropriate form of the expression that would reveal the time in minutes when the trough is empty.

•  $12(0)^2−13(0)+3$  

•  $(3x−1)(4x−3)$  

•  $12(x−3)^2−1$  

•  $2(x−1)^2−3$  

(8.01) The function $h(t)=−5t^2+25t$ shown in the graph models an architectural arch:

What is the domain of h(t)?

• All real numbers

• x ≥ 0

• 0 ≤ x ≤ 5

• 0 ≤ x ≤ 31

(8.01) A function is shown: $f(x)=16x^2−1.$  
Choose the equivalent function that best shows the x-intercepts on the graph.

• f(x) = (4x + 1)(4x − 1)

• f(x) = (8x + 1)(8x − 1)

•  $f(x)=4(x^2+1)$  

•  $f(x)=8(x^2−1)$  

(8.01) Abby collected data modeling a company's costs versus its profits. The data are shown in the table:

Which of the following is a true statement for this function?

• The function is decreasing from x = −3 to x = −1.

• The function is increasing from x = −3 to x = −1.

• The function is decreasing from x = −1 to x = 0.

• The function is decreasing from x = 0 to x = 2.

(8.01) Jordan is kayaking upstream. The following equation models his speed: $f(x)=2x^2−4x−9$ , where x is Jordan's speed relative to land. What is the domain of the function?

• x ≥ 1

• x ≤ −4

• x ≥ −9

• All real numbers

(8.01) Which of the following is the graph of $f(x)=x^2−5x+4?$  

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