A movie theatre sells tickets for $8.50 each. The manager is considering raising the prices but knows that for every 50 cents the price is raised, 20 fewer people go to the movies. The equation R = -40c^2 = 720c describes the relationship between the cost of tickets, c dollars, and the amount of revenue, R dollars, that the theatre makes. What price should the theatre charge to maximize revenue? I believe what I need to do is find the maximum vertex of the parabola in order to solve the equation. So I did the following: R = -40c^2 - 720c = -40(c^2 - 18c) = -40(c^2 - 18c + 9^2 - 9^2) <-- complete the square = -40(c^2 - 18c + 81 - 81) = -40[(c^2 - 9)^2 - 81) = -40(c^2 - 9)^2 + 3240 Which would give me a vertex (9, 3240) but this does not make sense to me, I am not sure what I am looking for to be honest. I believe that the maximum price would be $9.00 to have a revenue of $3240, is this correct and I am just second guessing?