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Sun 1 Jan, 2006 05:53 am
I have a question on logarithmic function.
Let the profit in selling x jackets be fiven by the function g(x).
If the profit in selling (x + 10) jackets = - (x)^2 + 100 x -1600. Find the function g (x). Express the ans in the form a(x- h)^2 + k.)
Strange function by the way - if I sell 0 jackets I make a loss, if I sell infinite jackets I make infinite loss, don't think I'd like this business model.
So f(x+10) = -x^2 + 100x - 1600
let y = x+10 or x = y - 10
f(y) = -(y - 10)^2 + 100(y-10) - 1600
= -y^2 + 20y -100 + 100y -1000 - 1600
= -y^2 + 120y - 2700
= -(y - 60)^2 + 900
hence f(x) = -(x - 60)^2 + 900
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