Question 357524
1. find the roots by setting P(x) equal to zero ___ -x^2 + 812x - 9600 = 0
___ dividing by -1 ___ x^2 - 812x + 9600 = 0
___ factoring ___ (x - 12)(x - 800) = 0
___ the roots are 12 and 800
___ the lower number represents the break even point where the costs equal the sales
___ the higher number probably represents market saturation (I do math, not finance)
to much product for the market and the price declines (and/or sales drop), causing profits to fall


2. the min (or max, in this case) lies midway between the roots (their average)
___ (800 + 12) / 2 = 406


3. plug 406 into the profit function ___ P(406) = -406^2 + 812(406) - 9600


4. the x-coordinate of the vertex is 406 , the y-coordinate is the answer from #3
___ this represents the max profit and the number of sets needed to achieve it



the axis of symmetry passes through the vertex
___ it is a vertical line whose equation is ___ x = 406



the parabola opens downward
it passes through the roots and the vertex (which is the "nose" of the parabola)
the axis of symmetry is the midline of the parabola