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

Answer 1

Perimeter = 300

Area = a(w)

Width = w

Perimeter = 300 and width = w ⇒ length = [300 - 2w ]/2 = 150 - w

Area, A = width * length = w(150-w) = 150w -w^2

Roots = w = 0 and w =150
Vertex
           w =[0 + 150]/2 = 75
           A = 75(150-75) = 75^2 = 5625

           (75,5625)

Given that the coefficient of w^2 is negative, the vertex is the maximum of the function or area.

The second coordinate of the vertex (5625) is the maximum area the fence can enclose.

Answer: the maximum area that can be enclosed by the fencing.
 Hope this helps!