Respuesta :
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.
