A.6.7.2 What Price to Charge?

A company that sells movies online is deciding how much to charge customers to download a new movie. Based on data from previous sales, the company predicts that if they charge x dollars for each download, then the number of downloads, in thousands, is 18 - x. Complete the table to show the predicted number of downloads at each listed price. Then, find the revenue at each price. The first row has been completed for you.

Is the relationship between the price of the movie and the revenue (in thousands of dollars) quadratic? Explain how you know. Then, Plot the points that represent the revenue, r, as a function of the price of one download in dollars, x.

What price would you recommend the company charge for a new movie? Explain your reasoning.

If we graph the equation r = x(18 - x) using graphing technology, it would produce a graph like this: What domain is appropriate for the price of a new movie?

What are the zeros of the function? What do they tell us in this situation?

What is the vertex of the graph representing the function? What does it tell us in this situation?