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Shenelle has 100 100 meters of fencing to build a rectangular garden. The garden's area (in square meters) as a function of the garden's width x x (in meters) is modeled by: A(x)=−(x−25)2+625 A(x) = -(x - 25)^2 + 625 What is the maximum area possible?

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Q. Shenelle has 100 100 meters of fencing to build a rectangular garden. The garden's area (in square meters) as a function of the garden's width x x (in meters) is modeled by: A(x)=−(x−25)2+625 A(x) = -(x - 25)^2 + 625 What is the maximum area possible?
  1. Given Area Function: We are given the area function A(x)=−(x−25)2+625A(x) = -(x - 25)^2 + 625. This is a quadratic function in the form of a parabola that opens downwards (since the coefficient of the squared term is negative). The maximum value of this function will be at its vertex.
  2. Find Vertex: To find the vertex of the parabola, we look at the function A(x)=−(x−25)2+625A(x) = -(x - 25)^2 + 625. The vertex form of a parabola is given by y=a(x−h)2+ky = a(x - h)^2 + k, where (h,k)(h, k) is the vertex of the parabola. In our case, h=25h = 25 and k=625k = 625, so the vertex is at (25,625)(25, 625).
  3. Maximum Area: The vertex (25,625)(25, 625) represents the maximum point on the parabola because the coefficient of the squared term is negative, indicating that the parabola opens downwards. Therefore, the maximum area possible for the garden is 625625 square meters.

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