Question

A company's profit is described by the equation P(x)=-5x^2+300x+15,000

Answer 1

When x=30 units, y = profit = -5(30)^2 + 300(30) + 15000 = $19500

Answer 2

P(x)=-5x^2+300x+15,000 is the equation of a parabola and represents profit.  Its graph opens down.  Our job is to find the x-coordinate of the vertex (which is the x-coord of the maximum profit) and then the corresponding y-value.

The formula x = -b / (2a) will produce that x-coordinate:

        -(300)
x = ------------ = 30
         2(-5)

When x=30 units, y = profit = -5(30)^2 + 300(30) + 15000 = $19500  (answer)