Question 919259
Format ax^2 + bx + c
the vertex form of a Parabola opening up(a>0) or down(a<0), {{{y=a(x-h)^2 +k}}}
P(x)=-x^2+720x-14000 |parabola opening downward:  a = -1 < 0
complete Square
p(x) = -(x-360)^2 + (360)^2 - 14000 |Note 360 = 720/-2a = b/-2a
x = 360 is the x-value of the vertex of this parabola opening downward
x = b/-2a = 360, max profit
..........

For what values of X does the complex produce a profit
P(x)= -x^2+720x-14000 > 0
-(x-360)^2 + (360)^2 - 14000 = 0
(x-360)^2 = (360)^2 - 14000
(x-360)^2 = 115600
x - 360 = ± 340
x = 360 ± 340
x-intercepts are 20, 700
20 < x < 700 produces a profit (x = 360 being the max profit value)
..........
0r by factoring
-x^2+720x-14000 = 0
x^2-720x+14000
(x-20)(x-700) = 0  Same results, of course.
{{{drawing(300,300,   -100,1000,-10000,125000,    
 grid(1),
circle(360, 115600,10),

graph( 300, 300, -100,1000,-10000,125000,0, -x^2+720x-14000))}}}