Beth wants to plant a garden at the back of her house. she has 32m of fencing. the area that can be enclosed is modelled by the function a(x) = -2x2 + 32x, where x is the width of the garden in metres and a(x) is the area in square metres. what is the maximum area that can be enclosed?
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The maximum area that can be obtained by the garden is 128 meters squared.

Step-by-step explanation:

A represents area and we want to know the maximum.

is a parabola.  To find the maximum of a parabola, you need to find it's vertex.  The y-coordinate of the vertex will give us the maximum area.

To do this we will need to first find the x-coordinate of our vertex.

to then .

To find the y that corresponds use the equation that relates y and x.

The maximum area that can be obtained by the garden is 128 meters squared.