# Building Quadratic Functions to Describe Situations (Part 2)

ID: roziz-gifup Illustrative Mathematics, CC BY 4.0
Subject: Algebra, Algebra 2

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 ﻿$h(t)=-5t^2 +10t+3$﻿, where ﻿$t$﻿ is time measured in seconds and ﻿$h(t)$﻿ is measured in meters. Select ﻿$\textbf{all}$﻿ 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 ﻿$h$﻿ 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 ﻿$h$﻿ given by the equation ﻿$h(t)=3+60t-16t^2$﻿. The graph of the function is shown. 2) About when does the baseball reach its maximum height?

Show Work

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

Show Work

4) About when does the ball hit the ground?

Show Work
##### Problem 3

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

5) Determine which rock hits the ground first.

Show Work

6) Explain how you know.

##### Problem 4

Each expression represents an object’s distance from the ground in meters as a function of time,﻿$t$﻿, in seconds.

Object A: ﻿$-5t^2+25t+50$﻿

Object B: ﻿$-5t^2+50t+25$﻿

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

Show Work

8) Which object was launched from the greatest height?

Show Work
##### 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. Determine the area for these possible lengths and widths.

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

Show Work

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

Show Work

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

Show Work

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

Show Work

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

Show Work

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

##### Problem 6

Here is a pattern of dots. 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 ﻿$n$﻿?

##### Problem 7

The function ﻿$f$﻿ is defined by ﻿$f(x)=2^x$﻿ and the function ﻿$g$﻿ is defined by ﻿$g(x)=x^2+16$﻿.

21) Find the value of ﻿$f$﻿ when ﻿$x$﻿ is 4.

Show Work

22) Find the value of ﻿$f$﻿ when ﻿$x$﻿ is 5.

Show Work

23) Find the value of ﻿$f$﻿ when ﻿$x$﻿ is 6.

Show Work

24) Find the value of ﻿$g$﻿ when ﻿$x$﻿ is 4.

Show Work

25) Find the value of ﻿$g$﻿ when ﻿$x$﻿ is 5.

Show Work

26) Find the value of ﻿$g$﻿ when ﻿$x$﻿ is 6.

Show Work

27) Will the values of ﻿$f$﻿ always be greater than the values of ﻿$g$﻿?

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 ﻿$d=32-5t^2$﻿ gives the distance from the ground,﻿$d$﻿, in meters after ﻿$t$﻿ seconds.

Find ﻿$d$﻿ given values for ﻿$t$﻿.

29) ﻿$t \ = \ 0$﻿

Show Work

30) ﻿$t \ = \ 0.5$﻿

Show Work

31) ﻿$t \ = \ 1$﻿

Show Work

32) ﻿$t \ = \ 1.5$﻿

Show Work

33) ﻿$t \ = \ 2$﻿

Show Work

34) Plot the data on the coordinate plane. 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. 37) Write an equation giving the number of mcg of insulin,﻿$m$﻿, in the patient's body ﻿$h$﻿ 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.