Change the quadratic form from standard form to vertex form y=x^2-8x+15

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.

the maximum area that can be enclosed by the fencing