Building Quadratic Functions to Describe Situations (Part 2)

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Created by Illustrative MathematicsIllustrative Mathematics, CC BY 4.0
Subject: Algebra, Algebra 2
Grade: 8-9
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39 questions

Building Quadratic Functions to Describe Situations (Part 2)

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Problem 1

1) The height of a diver above the water, is given by h(t)=5t2+10t+3h(t)=-5t^2 +10t+3, where tt is time measured in seconds and h(t)h(t) is measured in meters. Select all\textbf{all} statements that are true about the situation. Write each corresponding letter in the answer box and separate letters with commas.

a) The diver begins 5 meters above the water.

b) The diver begins 3 meters above the water.

c) The function has 1 zero that makes sense in this situation.

d) The function has 2 zeros that make sense in this situation.

e) The graph that represents hh starts at the origin and curves upward.

f) The diver begins at the same height as the water level.

Problem 2

The height of a baseball, in feet, is modeled by the function hh given by the equation h(t)=3+60t16t2h(t)=3+60t-16t^2. The graph of the function is shown.

A template for answering this question. Ask your instructor for an alternative.

2) About when does the baseball reach its maximum height?

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3) About how high is the maximum height of the baseball?

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4) About when does the ball hit the ground?

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Problem 3

Two rocks are launched straight up in the air. The height of Rock A is given by the function ff, where f(t)=4+30t16t2f(t) = 4 + 30t - 16t^2. The height of Rock B is given by gg, where g(t)=5+20t16t2g(t) = 5 + 20t - 16t^2. In both functions, tt is time measured in seconds and height is measured in feet.

5) Determine which rock hits the ground first.

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6) Explain how you know.

Problem 4

Each expression represents an object’s distance from the ground in meters as a function of time,tt, in seconds.

Object A: 5t2+25t+50-5t^2+25t+50

Object B: 5t2+50t+25-5t^2+50t+25

7) Which object was launched with the greatest vertical speed?

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8) Which object was launched from the greatest height?

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Problem 5

Tyler is building a pen for his rabbit on the side of the garage. He needs to fence in three sides and wants to use 24 ft of fencing.

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Determine the area for these possible lengths and widths.

9) Length (ft) = 8, Widths (ft) = 8, Area (ft2^2) =

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10) Length (ft) = 10, Widths (ft) = 7, Area (ft2^2) =

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11) Length (ft) = 12, Widths (ft) = 6, Area (ft2^2) =

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12) Length (ft) = 14, Widths (ft) = 5, Area (ft2^2) =

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13) Length (ft) = 16, Widths (ft) = 4, Area (ft2^2) =

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14) Which length and width combination should Tyler choose to give his rabbit the most room?

Problem 6

Here is a pattern of dots.

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15) What is the total number of dots in Step 0?

16) What is the total number of dots in Step 1?

17) What is the total number of dots in Step 2?

18) What is the total number of dots in Step 3?

19) How many dots will there be in Step 10?

20) How many dots will there be in Step nn?

Problem 7

The function ff is defined by f(x)=2xf(x)=2^x and the function gg is defined by g(x)=x2+16g(x)=x^2+16.

21) Find the value of ff when xx is 4.

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22) Find the value of ff when xx is 5.

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23) Find the value of ff when xx is 6.

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24) Find the value of gg when xx is 4.

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25) Find the value of gg when xx is 5.

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26) Find the value of gg when xx is 6.

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27) Will the values of ff always be greater than the values of gg?

True or false? Write below.

28) Explain how you know.

Problem 8

Han accidentally drops his water bottle from the balcony of his apartment building. The equation d=325t2d=32-5t^2 gives the distance from the ground,dd, in meters after tt seconds.

Find dd given values for tt.

29) t = 0t \ = \ 0

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30) t = 0.5t \ = \ 0.5

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31) t = 1t \ = \ 1

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32) t = 1.5t \ = \ 1.5

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33) t = 2t \ = \ 2

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34) Plot the data on the coordinate plane.

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35) Is the water bottle falling at a constant speed?

True or false? Write below.

36) Explain how you know.

Problem 9

The graph shows how much insulin, in micrograms (mcg), is in a patient's body after receiving an injection.

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37) Write an equation giving the number of mcg of insulin,mm, in the patient's body hh hours after receiving the injection.

38) After 3 hours, will the patient still have at least 10 mcg of insulin in their body?

True or false? Write below.

39) Explain how you know.