Question 466677
Revenue = price*quantity
Typically the higher the price the less likely someone will buy the product
Or in other words there is less demand
At a low price, quantity may be high but overall revenue will be low
As price increases, revenue increases 
However, at some point the price will increase too much such that the quantity becomes too low and the overall revenue will start decreasing
This is the optimal price for maximum revenue.
At a very high price, quantity will be very low and revenue will be low as well
Thus the inverse relationship between price and quantity yields a parabolic revenue curve.
To find maximum, determine vertex of the graph.
Given quadratic equation of the form:
{{{ax^2 + bx + c}}}
the x_coordinate of the vertex or line of symmetry is:
{{{x = -b/2a}}}
For our revenue function:
a = -15
b = 300
c = 1200
{{{x = (-300)/(2*-15)}}}
{{{x = (-300)/-30}}}
{{{x = 10}}}
To find y_coordinate, substitute 10 into function
{{{y = -15(10^2) + 300(10) + 1200}}}
{{{y = -1500 + 3000 +1200}}}
{{{y = 2700}}}
Vertex is at (10, 2700)
Thus max revenue is $2700 at a price of $10