Graph the equation.
y= 1/8(x-6)(x+2)

  see below

Step-by-step explanation:

See the attachment.

The graph will have x-intercepts where the factors are zero, at x=6 and x=-2. The y-intercept will be the value when x=0: (1/8)(-6)(2) = -1.5.

The axis of symmetry is halfway between the zeros, so is x = (6-2)/2 = 2.

The minimum value of the function is at x=2, so is ...

  y = (1/8)(2 -6)(2 +2) = 1/8(-16) = -2

Other y-values can be found by substituting other x-values in the equation and evaluating it. Rather than go to that trouble, I prefer to use a graphing calculator.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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step-by-step explanation: