Question

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 minimum width that can be used for the fencing
the maximum area that can be enclosed by the fencing
the width that gives the maximum area
the length that gives the maximum area

Answer 1

9514 1404 393

Answer:

the maximum area that can be enclosed by the fencing

Explanation:

If the width of the garden is w (in yards), then the length of the garden is (150-w) and the area is ...

A(w) = w(150 -w) = -(w² -150w)

A(w) = -(w² -150w +75²) +75²

A(w) = -(w -75)² +5625

In this vertex form, the vertex is (75, 5625).

The graph of area versus width is a parabola that opens downward, so the vertex second coordinate is the maximum area that can be enclosed.