![]() The function, written in general form, is This formula represents the area of the fence in terms of the variable length. We know the area of a rectangle is length multiplied by width, so Now we are ready to write an equation for the area the fence encloses. This allows us to represent the width,, in terms of. ⒶWe know we have only 80 feet of fence available, and, or more simply. It is also helpful to introduce a temporary variable,, to represent the width of the garden and the length of the fence section parallel to the backyard fence. Let's use a diagram such as Figure 10 to record the given information. ![]() ⒷWhat dimensions should she make her garden to maximize the enclosed area? ⒶFind a formula for the area enclosed by the fence if the sides of fencing perpendicular to the existing fence have length. She has purchased 80 feet of wire fencing to enclose three sides, and she will use a section of the backyard fence as the fourth side. There are many real-world scenarios that involve finding the maximum or minimum value of a quadratic function, such as applications involving area and revenue.įinding the Maximum Value of a Quadratic FunctionĪ backyard farmer wants to enclose a rectangular space for a new garden within her fenced backyard. We can see the maximum and minimum values in Figure 9. The output of the quadratic function at the vertex is the maximum or minimum value of the function, depending on the orientation of the parabola. ![]() Determining the Maximum and Minimum Values of Quadratic Functions
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