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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. - PowerPoint PPT Presentation
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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.