Have you ever wondered how to make the most money owning a movie theater?

For example, if changing the ticket price changes the number of customers, what is

the best ticket price?

In this lesson you will learn how to create and graph

relationships by using quadratic functions

Let’s Review

Quadratic Functions are graphed as parabolas

vertex

x2 + 3 = 52x2 – 4x = y-4x2 -9x + y = 0

A Common Mistake

Mixing up your inputs and outputs.

Cost Profit

12 90

10 80

9 75

5 55

Cost? Profit? Which is our input?

Core Lesson

Let’s investigate the following:You are the owner of a movie theater, and you

charge $8 per ticket, with an average of 40 people at each show. For each dollar increase in your ticket price, you can expect to lose 4 customers. Create and graph an expression, and then describe the relationship between

ticket price increases and revenue.

Core Lesson

r = p*t

r = (8+x) * tr = (8+x)(40-4x)

revenue = price * tickets

price = 8 + 1xtickets = 40-4x

r = -4x2 + 8x + 320

Core Lesson

Input (x) Output (r)

0 320

1 324

2 320

3 308

4 288

10 0

r = -4x2 + 8x + 320

-100

100

300

500

0 2 4 6 8 10Price changes(#)

Reven

ue (

$)

In this lesson you have learned how to create and graph

relationships by using quadratic functions

Guided Practice

Let’s investigate the following:An apartment rental agency has 50

apartments rented out in a building; each rents for $450. They know that for each $30 increase in rent, 2 less apartments will be

rented. Create and graph an expression that describes the relationship between the number of price changes and revenue.

Guided Practice

r = p*a

r = (450+30x) * a

r = (450+30x)(50-2x)

revenue = price * apartments

price = 450+30x

apartments = 50-2x

r = -60x2 +600x + 22500

Guided Practice

Input (x) Output (r)

0 22500

1 23040

2 23460

3 23760

4 23940

5 24000

6 23940

7 23760

r = -60x2 + 600x + 22500

0

10000

20000

30000

0 2 4 6 8 10

Reven

ue (

$)

Price changes(#)

Extension Activities

1. Try finding the equation for each function using a table of values to find the vertex and y-intercept. Compare to the original functions we created on these videos

2. Explore how adjusting price/customer changes can affect the revenue function.

3. Use the computer to explore a real-life “maximization” and present to your classmates what the function is, and how it is similar/different to those learned here.

Quick Quiz

1. Chuck own a roller-skating rink and charges $12 per person. On average, 36 people attend each day. He knows that an increase in price of 50 cents will cause him to lose 2 customers per day. Create and graph the function that describes the relationship between price change and revenue.

2. Airline Q sells an average of 100 seats per flight to California, at a price of $200 each. For each $20 decrease in cost, they increase the number of passengers by 2. Create and graph the function that describes the relationship between price change and revenue.