SOLUTION: hello i submitted these questions and get answer but what i needed to know was HOW do we get the answers I want to see the work so i learn, so i am resubmitting hoping for this: I

Question 357524: hello i submitted these questions and get answer but what i needed to know was HOW do we get the answers I want to see the work so i learn, so i am resubmitting hoping for this:
I have been working on this all week and I just cannot get it. I know this is short notice but it is due with in the next 12 hours PLEASE HELP!
A plasma TV company determines that its total profit on the production and sale of x TVs is given by: P(x)= -x^2+812x-9600
the question that i am stuck on are as follows, and i have to show the work:
1. Find the solutions and explain what these solutions represent.
2. How many TV�s must be produced to reach a minimum or maximum profit?
3.What is this minimum or maximum profit?
4.What is the vertex of this graph? How is this point related to your answers from e and f?
I also have to graph this function. Include solutions (roots), vertex, axis of symmetry, and labels for each.

Thanks in advance
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
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
RELATED QUESTIONS
Hello, What about if I know some values for x and y and I want the function? Example: I... (answered by Alan3354)

Hi there! I just started highschool at a collegiate school. I am so thankful I got in,... (answered by Alan3354,ikleyn)

I submitted this question earlier but there was a typo I apologize to whoever read it.... (answered by jim_thompson5910)

I am having trouble. I am in college algebra and we are having to simplify rational... (answered by stanbon,algebrahouse.com)

I am trying to help my 9th grade brother with his homework. He does not have his text... (answered by checkley71)

This is under equations of lines - Hi I'm a mom trying really hard to help her child with (answered by Theo)

If three times the supplement of an angle is subtracted from seven times the complement... (answered by addingup)

i dont want to know the answer i just want to know what i need to do to get the answer (answered by ankor@dixie-net.com)

An explanation to my question would be greatly appreciated. I have many of these... (answered by MathTherapy)