Question

A theatre owner is trying to decide on a ticket price for his next play. The higher the price, the fewer the number of people who will buy tickets. He creates a quadratic function f(x) to estimate his total revenue, in dollars, if he charges x dollars per ticket. Then, he creates a table of values.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The quadratic function he creates is f(x) = -2x^2 + 100x.

Table of values:
x = 0, f(0) = 0
x = 10, f(10) = -2(10)^2 + 100(10) = -200 + 1000 = 800
x = 20, f(20) = -2(20)^2 + 100(20) = -800 + 2000 = 1200
x = 30, f(30) = -2(30)^2 + 100(30) = -1800 + 3000 = 1200
x = 40, f(40) = -2(40)^2 + 100(40) = -3200 + 4000 = 800
x = 50, f(50) = -2(50)^2 + 100(50) = -5000 + 5000 = 0

Based on the table, the theatre owner can see that his revenue is highest when he charges $20 per ticket. At this price, he can expect to make $1200 in total revenue.