# Thread: maximum profit? quadratic function??

1. ## maximum profit? quadratic function??

I'm quite confused on this word problem.... I know I have to complete the square, right? But, I'm not certain:

please also supply work! i have many more questions like this and shall use this one as a template to solve the rest!

thank you so much!

2. Originally Posted by lollilikeslife
I'm quite confused on this word problem.... I know I have to complete the square, right? But, I'm not certain:

please also supply work! i have many more questions like this and shall use this one as a template to solve the rest!

thank you so much!
The given function P is a parabola opening down. Therefore the absolute maximum is at it's vertex.

I don't know which method you prefer to determine the vertex, but since you mentioned completing the square, here we go:

$\displaystyle P(x)=-0.5x^2+20x+230=-0.5(x^2-40x+400-400)+230$

$\displaystyle \ \ \ =-0.5(x-20)^2+200+230 = \boxed{-0.5(x-20)^2+430}$

Thus the maxium is 430 at x = 20