Question

shenelle has 100 meters of fencing to build a rectangular garden. the gardens area (in square meters) as a function of the gardens width ( x ) (in meters) is modeled by: ( a(x) = -(x - 25)^2 + 625 ) what is the maximum area possible? (square) square meters show calculator

Explanation:

Step1: Analyze the function form

The area function is given in vertex form \( A(x)=-(x - 25)^2+625 \). The vertex form of a quadratic function is \( y = a(x - h)^2 + k \), where \((h,k)\) is the vertex of the parabola.

Step2: Determine the maximum value

For a quadratic function \( y = a(x - h)^2 + k \), if \( a<0 \), the parabola opens downwards, and the vertex \((h,k)\) is the maximum point. In the function \( A(x)=-(x - 25)^2+625 \), \( a=- 1<0 \), so the vertex \((25,625)\) gives the maximum value of the function. The \( k \)-value of the vertex is the maximum area.

Answer:

625