Question 1173633
your formula is:


y = (600 - 30x) * (6 + .5x) 


y is the revenue


600 - 30x tells you the number of new subscriptions sold each week.


6 + .5x tells you the price of each new subscription, in dollars.


the value of x tells you the number of times you are subtracting 30 from 600 and adding .5 to 6.


when x = 0, the number of subscriptions remains at 600 and the price remains at 6 and the revenue becomes 600 * 6 = 3600.


when x = 1, the number of subscriptions becomes 570 and the price per subscription becomes 6.5 and the revenue becomes 570 * 6.5 = 3705.


y = (600 - 30x) * (6 + .5x) is a quadratic equation.


the standard form of this equation is y = -15x^2 + 120x + 3600


with the equation in standard form, a is the coefficient of the x^2 term and b is the coefficient of the x term and c is the constant term.


the maximum value of this quadratic equation is when x = -b / 2a
that becomes -120 / -30 = 4.


when x = 4, y = -15x^2 + 120x + 3600 becomes y = -15 * 16 + 120 * 4 + 3600 which becomes -240 + 480 + 3600 = 3840.


this can be seen in the graph of the two equivalent equations.


because they are equivalent, they draw the same curve on the graph.


the two equivalent equations are:


y = (600 - 30x) * (6 + .5x) 
y = -15x^2 + 120x + 3600


here's the graph.


<img src = "http://theo.x10hosting.com/2021/012401.jpg" >