Quadratic Functions

A quadratic function can be written as f of x equals a x squared plus b x plus c, where a, b, and c are real numbers, and a is not zero. Its domain is usually all real numbers, but a real-life quadratic model may have a restricted domain.

For example, imagine a baseball team playing in a stadium with 40,000 seats, where tickets can cost up to $40. The ticket price affects the expected attendance, which in turn affects ticket revenue.

To model this relationship, suppose that at a ticket price of t dollars, the expected attendance is 60,000 minus 1,000t. Multiplying this by the ticket price gives the quadratic revenue function R of t.

Since the stadium holds at most 40,000 spectators, the expected attendance must be less than or equal to 40,000.

Solving this inequality gives t greater than or equal to 20. With a maximum ticket price of $40, the revenue function has a domain of 20 to 40, including both endpoints.

Within this domain, the function can be used to compare ticket prices and predict ticket revenue.