# Building Quadratic Functions to Describe Situations (Part 1)

ID: lotul-kuvuz Illustrative Mathematics, CC BY 4.0
Subject: Algebra, Algebra 2

22 questions

# Building Quadratic Functions to Describe Situations (Part 1)

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##### Problem 1

1) A rocket is launched in the air and its height, in feet, is modeled by the function ﻿$h$﻿. Below is a graph representing ﻿$h$﻿.

Select ﻿$\textbf{all}$﻿ true statements about the situation. Write each corresponding letter in the answer box and separate letters with commas.

a) The rocket is launched from a height less than 20 feet above the ground.

b) The rocket is launched from about 20 feet above the ground.

c) The rocket reaches its maximum height after about 3 seconds.

d) The rocket reaches its maximum height after about 160 seconds.

e) The maximum height of the rocket is about 160 feet. ##### Problem 2

A baseball travels ﻿$d$﻿ meters ﻿$t$﻿ seconds after being dropped from the top of a building. The distance traveled by the baseball can be modeled by the equation ﻿$d=5t^2$﻿.

Determine the ﻿$d$﻿, in meters, at the given times.

2) ﻿$t = 0$﻿seconds

Show Work

3) ﻿$t = 0.5$﻿ seconds

Show Work

4) ﻿$t = 1$﻿ second

Show Work

5) ﻿$t = 1.5$﻿ seconds

Show Work

6) ﻿$t = 2$﻿ seconds

Show Work

7) Plot the data on the coordinate plane. 8) Is the baseball traveling at a constant speed?

True or false? Write below.

9) Explain how you know.

##### Problem 3

10) A rock is dropped from a bridge over a river. Which table could represent the distance in feet fallen as a function of time in seconds? a)

Table A

b)

Table B

c)

Table C

d)

Table D

##### Problem 4

Determine whether ﻿$5n^2$﻿ or ﻿$3^n$﻿ will have the greater value when:

11) ﻿$n=1$﻿

Show Work

12) ﻿$n=3$﻿

Show Work

13) ﻿$n=5$﻿

Show Work
##### Problem 5

14) Select ﻿$\textbf{all}$﻿ of the expressions that give the number of small squares in Step ﻿$n$﻿. Write each corresponding letter in the answer box and separate letters with commas.

a) ﻿$2n \quad \quad$﻿ b) ﻿$n^2 \quad \quad$﻿ c) ﻿$n+1 \quad \quad$﻿ d) ﻿$n^2+1 \quad \quad$﻿ e) ﻿$n(n+1) \quad \quad$﻿ f) ﻿$n^2+n \quad \quad$﻿ g) ﻿$n+n+1 \quad \quad$﻿ ##### Problem 6

15) A small ball is dropped from a tall building. Which equation could represent the ball’s height,﻿$h$﻿, in feet, relative to the ground, as a function of time,﻿$t$﻿, in seconds?

a)

﻿$h$﻿=100-16﻿$t$﻿

b)

﻿$h$﻿=100-16﻿$t^{2}$﻿

c)

﻿$h$﻿=100-16﻿$t^{t}$﻿

d)

﻿$h$﻿=100-﻿$\frac{16}{t}$﻿

##### Problem 7

16) Use the rule for function ﻿$f$﻿ to draw its graph.

﻿$f(x) = \begin{cases} 2, & -5 \leq x < -2 \\ 6, & -2 \leq x < 4 \\ x, & 4 \leq x < 8 \end{cases}$﻿ ##### Problem 8

Diego claimed that ﻿$10+x^2$﻿ is always greater than ﻿$2^x$﻿ and used this table as evidence.

﻿$\begin{array}{|c|c|c|} \hline \\[-1em] x & 10 + x^2 & 2^x \\[-1em] \\ \hline \\[-1em] 0 & 11 & 2 \\[-1em] \\ \hline \\[-1em] 0.5 & 14 & 4 \\[-1em] \\ \hline \\[-1em] 1 & 19 & 8 \\[-1em] \\ \hline \\[-1em] 1.5 & 26 & 16 \\[-1em] \\ \hline \end{array}$﻿

17) Do you agree with Diego?

True or false? Write below.

##### Problem 9

The table shows the height, in centimeters, of the water in a swimming pool at different times since the pool started to be filled.

﻿$\begin{array}{|c|c|} \hline \\[-1em] \textbf{minutes} & \textbf{height} \\[-1em] \\ \hline \\[-1em] 0 & 150 \\[-1em] \\ \hline \\[-1em] 1 & 150.5 \\[-1em] \\ \hline \\[-1em] 2 & 151 \\[-1em] \\ \hline \\[-1em] 3 & 151.5 \\[-1em] \\ \hline \end{array}$﻿

19) Does the height of the water increase by the same amount each minute?

True or false? Write below.

20) Explain how you know.

21) Does the height of the water increase by the same factor each minute?

True or false? Write below.

22) Explain how you know.