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IM Alg1.6.7 Practice: Building Quadratic Functions to Describe Situations (Part 3)

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

Complete the table to find out how many tickets the theater expects to sell and what revenues it expects to receive at the given ticket prices. 

For which ticket prices will the theater earn no revenue? Explain how you know.

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? Explain how you know.

A company sells running shoes. If the price of a pair of shoes in dollars is , the company estimates that it will sell pairs of shoes. Write an expression that represents the revenue in dollars from selling running shoes if a pair of shoes is priced at dollars.

The function represents the revenue in dollars the school can expect to receive if it sells coffee mugs for dollars each. Here is the graph of . Select all the statements that describe this situation.

Select all that apply
  • A
  • B
  • C
  • D
  • E
  • F
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Write an equation to represent the relationship between the step number, , and the number of small squares, . Briefly describe how each part of the equation relates to the pattern.

Is the relationship between the step number and number of small squares quadratic? Explain how you know.

A small marshmallow is launched straight up in the air with a slingshot. The function , given by the equation , describes the height of the marshmallow in meters as a function of time, , in seconds since it was launched. Use graphing technology to graph the function in the applet below. About when does the marshmallow reach its maximum height?

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

What domain makes sense for the function in this situation?

A rock is dropped from a bridge over a river.

Graph AGraph B

Graph CGraph D

Which graph could represent the distance fallen, in feet, as a function of time in seconds?

Select all that apply
  • A
  • B
  • C
  • D
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A bacteria population, , is modeled by the equation , where is the number of days since the population was first measured. Select all statements that are true in this situation.

Select all that apply
  • A
  • B
  • C
  • D
  • E
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