Question 419440
Suppose you have 80 ft of fence to enclose a rectangular garden.The function A=40x-x^2 gives you the area of the gardne in square feet where x is the width in feet.
a. What width,x, gives you the maximum garden area?
b. what is the maximum area?

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Standard form for parabola:y=(x-h)^2+k,(h,k) being the (x,y) coordinates of the vertex, from which you can determine the maximum or minimum and the x-coordinate where it occurs.

A=40x-x^2
A=-(x^2-40x)
complete the square
A=-(x^2-40x+400)+400
A=-(x-20)^2+400
ans:
The width which gives the maximum area=20 ft
The maximum area = 400 sq ft
With dimensions 20 ft by 20 ft=80 ft of fencing