Question

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

Answer 1

The maximum area possible for Shenelle's rectangular garden with the given amount of fencing is 625 square meters, which is the vertex of the quadratic function representing the area.

Step-by-step explanation:

To find the maximum area possible for Shenelle's rectangular garden with the given fencing, we can analyze the function A(w) = - (w - 25)² + 625. This is a quadratic function in the form of a parabola that opens downward, indicating that the vertex represents the maximum point on the graph.

Since the quadratic is in vertex form, A(w) = a(w - h)² + k, where (h, k) is the vertex of the parabola, we can see that the maximum area is at the vertex (25, 625). Therefore, the maximum area that Shenelle can achieve for her garden with the 100 meters of fencing is 625 square meters.