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

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.

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

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  1. 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?

  2. In this lesson you will learn how to create and graph relationships by using quadratic functions

  3. Quadratic Functions are graphed as parabolas x2 + 3 = 5 2x2 – 4x = y -4x2 -9x + y = 0 vertex

  4. Mixing up your inputs and outputs. Cost? Profit? Which is our input?

  5. 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.

  6. r = p*t revenue = price * tickets price = 8 + 1x r = (8+x) * t tickets = 40-4x r = (8+x)(40-4x) r = -4x2 + 8x + 320

  7. r = -4x2 + 8x + 320 500 300 Revenue ($) 100 0 2 4 6 8 10 - 100 Price changes(#)

  8. In this lesson you have learned how to create and graph relationships by using quadratic functions

  9. 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.

  10. r = p*a revenue = price * apartments price = 450+30x r = (450+30x) * a apartments = 50-2x r = (450+30x)(50-2x) r = -60x2 +600x + 22500

  11. r = -60x2 + 600x + 22500 30000 20000 Revenue ($) 10000 0 0 2 4 6 8 10 Price changes(#)

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

  13. 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.

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