SOLUTION: I am having a hard time solving this. Can you help? The profit function for selling x units of a certain product is given by {{{P(x)=-x^2+900x-160,000}}} A.)State the value o

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Question 948181: I am having a hard time solving this. Can you help?
The profit function for selling x units of a certain product is given by

A.)State the value of 'a', 'b,' and 'c' of the quadratic function P(x).
B.)Find the vertex of the graph of P(x).
C.)For what number of units is maximum profit achieved?
What is the maximum profit? Remember to include appropriate labels (units) in your answer.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
The comma interferes with the rendering. Your function is

(A):
P is given in general form so just read the values from the function definition as given.



(B) & (C):
You can put into standard form using completion of the square, but here is using the roots
and getting the midpoint value between them:

Roots of P,

Omitting the arithmetic simplification steps, your will find the roots to be

Now, what is the exact middle of those roots?
Find their sum, divide by 2, and find ...
that the axis of symmetry for P is at .

EVALUATE P at x=450.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
I am having a hard time solving this. Can you help?
The profit function for selling x units of a certain product is given by

A.)State the value of 'a', 'b,' and 'c' of the quadratic function P(x).
B.)Find the vertex of the graph of P(x).
C.)For what number of units is maximum profit achieved?
What is the maximum profit? Remember to include appropriate labels (units) in your answer.
A.



a =   - 1

b =   900

c = - 160



B.

x-coordinate of vertex is: x = , or , or , or 

y-coordinate of vertex is: , or 

Vertex: 



C.

Number of units that produces maximum profit: 

Maximum profit:  

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