Have to use the equation −0.75P² + 18P − 40 to solve for the amount of tickets.

Question

The football team is selling tickets to a football game and estimates that the team will earn −0.75P² + 18P − 40 dollars per game if they charge P dollars for tickets. What ticket price should the team charge in order to maximize its profits?

Answer 1

We recognize this as a parabola that opens at the bottom. It is a parabola because the highest exponent is the square. It opens at the bottom because the x² term has a negative coefficient.

So the x coordinate of the vertex is (-b / 2a) where a is -0.75 and b is 18

-b/ 2a = - (18) / 2 ( -0.75) = -18/ -1.5 which is 12. That is the amount the tickets must sell for.

To find the maximum intake, put 12 into the equation in place of p and evaluate.

Answer 2

f(P) = -075P² + 18P - 40

Transform into vertex form.

Values at vertex give number of tickets and the maximum intake.