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

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Mathematics

Sutton

7 August, 04:14

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

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Isla · 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