# Building Quadratic Functions to Describe Situations (Part 3)

ID: gilog-vufag
Illustrative Mathematics, CC BY 4.0
Subject: Algebra, Algebra 2

32 questions

# Building Quadratic Functions to Describe Situations (Part 3)

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##### Problem 1

Based on past musical productions, a theater predicts selling ﻿$400-8p$﻿ tickets when each ticket is sold at ﻿$p$﻿ dollars.

Determine how many tickets the theater expects to sell and what revenues it expects to receive at the given ticket prices.

Ticket Price (Dollars): 5

1) Number of Tickets Sold:

Show Work

2) Revenue (Dollars):

Show Work

Ticket Price (Dollars): 10

3) Number of Tickets Sold:

Show Work

4) Revenue (Dollars):

Show Work

Ticket Price (Dollars): 15

5) Number of Tickets Sold:

Show Work

6) Revenue (Dollars):

Show Work

Ticket Price (Dollars): 20

7) Number of Tickets Sold:

Show Work

8) Revenue (Dollars):

Show Work

Ticket Price (Dollars): 30

9) Number of Tickets Sold:

Show Work

10) Revenue (Dollars):

Show Work

Ticket Price (Dollars): 45

11) Number of Tickets Sold:

Show Work

12) Revenue (Dollars):

Show Work

Ticket Price (Dollars): 50

13) Number of Tickets Sold:

Show Work

14) Revenue (Dollars):

Show Work

Ticket Price (Dollars): ﻿$p$﻿

15) Number of Tickets Sold:

Show Work

16) Revenue (Dollars):

Show Work

17) For which ticket prices will the theater earn no revenue?

Show Work

18) Explain how you know.

19) At what ticket prices should the theater sell the tickets if it must earn at least $3,200 in revenue to break even (to not lose money) on the musical production? Show Work 20) Explain how you know. ##### Problem 2 21) A company sells running shoes. If the price of a pair of shoes in dollars is ﻿$p$﻿, the company estimates that it will sell ﻿$50,000-400p$﻿ pairs of shoes. Write an expression that represents the revenue in dollars from selling running shoes if a pair of shoes is priced at ﻿$p$﻿ dollars. Show Work ##### Problem 3 22) The function ﻿$f$﻿ represents the revenue in dollars the school can expect to receive if it sells ﻿$220-12x$﻿ coffee mugs for ﻿$x$﻿ dollars each. Below is the graph of ﻿$f$﻿. Select ﻿$\textbf{all}$﻿ the statements that describe the situation. Write each corresponding letter in the answer box and separate letters with commas. a) At$2 per coffee mug, the revenue will be $196. b) The school expects to sell 160 mugs if the price is$5 each.

c) The school will lose money if it sells the mugs for more than $10 each. d) The school will earn about$1,000 if it sells the mugs for $10 each. e) The revenue will be more than$700 if the price is between $4 and$14.

f) The expected revenue will increase if the price per mug is greater than \$10.

##### Problem 4

23) Write an equation to represent the relationship between the step number,﻿$n$﻿, and the number of small squares, ﻿$y$﻿.

24) Briefly describe how each part of the equation relates to the pattern.

25) Is the relationship between the step number and number of small squares quadratic?

True or false? Write below.

26) Explain how you know.

##### Problem 5

A small marshmallow is launched straight up in the air with a slingshot. The function ﻿$h$﻿, given by the equation ﻿$h(t)=5+20t-5t^2$﻿, describes the height of the marshmallow in meters as a function of time,﻿$t$﻿, in seconds since it was launched.

27) Graph the function ﻿$h$﻿. (Sketch the graph here.)

28) About when does the marshmallow reach its maximum height?

Show Work

29) About how long does it take before the marshmallow hits the ground?

Show Work

30) What domain makes sense for the function ﻿$h$﻿ in this situation?

##### Problem 6

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

a)

Graph A

b)

Graph B

c)

Graph C

d)

Graph D

##### Problem 7

32) A bacteria population,﻿$p$﻿, is modeled by the equation ﻿$p=100,000\cdot 2^d$﻿, where ﻿$d$﻿ is the number of days since the population was first measured.

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

a) ﻿$100,000\cdot 2^{-2}$﻿ represents the bacteria population 2 days before it was first measured.

b) The bacteria population 3 days before it was first measured was 800,000.

c) The population was more than 1,000 one week before it was first measured.

d) The population was more than 1,000,000 one week after it was first measured.

e) The bacteria population 4 days before it was first measured was 6,250.