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?Please help :(

Answer: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.[tex]A(x)=-2x^2+32x[/tex] 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.[tex]x=\frac{-b}{2a}{/tex] will give us the x-coordinate of the vertex.Compare [tex]-2x^2+32x[/tex] to [tex]ax^2+bx+c[/tex] then [tex]a=-2,b=32,c=0[tex].So the x-coordinate is [tex]\frac{-(32)}{2(-2)}=\frac{-32}{-4}=8[/tex].To find the y that corresponds use the equation that relates y and x.[tex]y=-2x^2+32x[/tex][tex]y=-2(8)^2+32(8)[/tex][tex]y=-2(64)+32(8)[/tex][tex]y=-128+256[/tex][tex]y=128[/tex]The maximum area that can be obtained by the garden is 128 meters squared.