SOLUTION: The manager of a large apartment complex has found that the profit is given by P(x)=-x^2+720x-14000, where x is the number of apartments rented. For what values of X does the comp

Algebra ->  Inequalities -> SOLUTION: The manager of a large apartment complex has found that the profit is given by P(x)=-x^2+720x-14000, where x is the number of apartments rented. For what values of X does the comp      Log On


   

Question 919259: The manager of a large apartment complex has found that the profit is given by P(x)=-x^2+720x-14000,
where x is the number of apartments rented. For what values of X does the complex produce a profit
Ive been stuck on this forever and I need help. I have a test coming up soon and I dont know how to do this type of problem
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Format ax^2 + bx + c
the vertex form of a Parabola opening up(a>0) or down(a<0), y=a%28x-h%29%5E2+%2Bk
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.