The perimeter of a rectangle is 540ft. Let x represent the width of the rectangle. Write a quadratic function for the area of rectangle in terms of its width. Find the vertex of the graph of the quadratic function and interpret its meaning in the context of the problem.

Answer 1

the length is 270-x

So, the area is length*width, or

f(x) = x(270-x)

As with all parabolas, the vertex is midway between the roots, so in this case, it's at x=135.

Since the graph opens downward, the vertex represents the maximum possible area.