Building Quadratic Functions to Describe Situations (Part 3)

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Created by Illustrative MathematicsIllustrative Mathematics, CC BY 4.0
Subject: Algebra, Algebra 2
Grade: 8-9
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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 4008p400-8p tickets when each ticket is sold at pp 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:

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2) Revenue (Dollars):

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Ticket Price (Dollars): 10

3) Number of Tickets Sold:

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4) Revenue (Dollars):

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Ticket Price (Dollars): 15

5) Number of Tickets Sold:

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6) Revenue (Dollars):

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Ticket Price (Dollars): 20

7) Number of Tickets Sold:

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8) Revenue (Dollars):

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Ticket Price (Dollars): 30

9) Number of Tickets Sold:

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10) Revenue (Dollars):

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Ticket Price (Dollars): 45

11) Number of Tickets Sold:

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12) Revenue (Dollars):

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Ticket Price (Dollars): 50

13) Number of Tickets Sold:

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14) Revenue (Dollars):

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Ticket Price (Dollars): pp

15) Number of Tickets Sold:

Show Work

16) Revenue (Dollars):

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

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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 pp, the company estimates that it will sell 50,000400p50,000-400p pairs of shoes.

Write an expression that represents the revenue in dollars from selling running shoes if a pair of shoes is priced at pp dollars.

Show Work
Problem 3

22) The function ff represents the revenue in dollars the school can expect to receive if it sells 22012x220-12x coffee mugs for xx dollars each.

Below is the graph of ff.

Select all\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.

A template for answering this question. Ask your instructor for an alternative.
Problem 4


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23) Write an equation to represent the relationship between the step number,nn, and the number of small squares, yy.

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 hh, given by the equation h(t)=5+20t5t2h(t)=5+20t-5t^2, describes the height of the marshmallow in meters as a function of time,tt, in seconds since it was launched.

27) Graph the function hh. (Sketch the graph here.)

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

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

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30) What domain makes sense for the function hh 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 template for answering this question. Ask your instructor for an alternative.
a)

Graph A

b)

Graph B

c)

Graph C

d)

Graph D

Problem 7

32) A bacteria population,pp, is modeled by the equation p=100,0002dp=100,000\cdot 2^d, where dd is the number of days since the population was first measured.

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

a) 100,00022100,000\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.