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, A(w). What does the second coordinate of the vertex of the quadratic function. A(w), represent?

The function A(w) gives the garden’s area for each width w, so the vertex’s first coordinate is a width and its second coordinate is an area. With 300 yards of fencing, the length is 150 − w, giving A(w) = w(150 − w), a downward-opening quadratic. Its vertex’s second coordinate is the greatest area the fencing can enclose, so the answer is “the maximum area that can be enclosed by the fencing.”

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