Three hundred yards of fencing is being used to fence in a rectangular garden. The area of the garden is modeled by a quadratic function of the rectangle’s width, cap A times w What does the second coordinate of the vertex of the quadratic function. cap A times w , represent?
Answer
A
the minimum width that can be used for the fencing
B
the length that gives the maximum area
C
the width that gives the maximum area
D
the maximum area that can be enclosed by the fencing
Explanation
With 300 yards of fencing, the rectangle’s length is 150 − w, so its area is A(w) = w(150 − w) = −w² + 150w. This quadratic opens downward, so the vertex gives the maximum area. The vertex’s second coordinate is that maximum area, so the correct choice is “the maximum area that can be enclosed by the fencing.”
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