Question 50100: I have the following problem and would appreciate some help getting started with it please. It is: The daily profit for a white goods company from the sale of bar fridges is given by P(x)= -x^2+40x+825. x is the number of bar fridges sold. find the function's vertex and intercepts.
I am assuming that a= -1, b=40 and c=825.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! P(x)= -x^2+40x+825
Rewrite as follows:
P(x)-825 = -(x^2-40x)
Complete the square as follows:
P(x)-825-400 = -(x^2-40x+400)
P(x)-1225 = -(x-20)^2
This follows the form 4p(y-k)=-(x-h)^2
where (h,k) is the vertex.
The vertex is (20,1225)
The P(x) intercept is (0,825)
The x-intercepts are:
x=[-40+-sqrt(40^2+4(825)]/-2
x=[-40+-70]/-2
x=(55,0), (-15,0)
Cheers,
Stan H.
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