Since the gardener has 440 ft of fencing, and only three sides of the garden need to be fenced, then we can use the perimeter formula. Draw a sketch of a rectangle. You could label the left and right sides of the rectangle as the L to represent the length, and the bottom of the rectangle could be W for the width, for example. The perimeter of the garden would be Perimeter = 2L + W = 440.
We have an equation with two variables, so we need another equation. The area of a rectangle can be found by multiplying length times width. If A = LW, then we could solve the equation above equation for W and use the Substitution Method to solve this system of linear equations. Solving the equation above for W gives us:
W = 440 - 2L
Substituting this into the area formula gives us: A = L(440 - 2L) = 440L - 2L²
This is a quadratic equation, which gives the graph of a parabola. The vertex of a parabola represents the maximum or minimum point. Since the coefficient of the squared term in this equation is negative, then the parabola will be concave down, and the vertex will be the maximum point.
Given a quadratic equation in standard f(x) = ax² + bx + c form, we can find the coordinates of the vertex (h, k) by the following formulas:
h = -b/2a
k = f(h)
