Question 888034
<pre>
Let y = cross-sectional area of trough:

{{{drawing(300,200,-3,3,-1,3,line(-2,0,2,0),line(-2,0,-2,2),line(2,0,2,2),
locate(-.5,0,8-2x),locate(2.1,1.2,x),locate(-2.2,1.2,x))}}}  {{{matrix(20,1,
matrix(1,3,y,""="",x(8-2x)),
matrix(1,3,y,""="",8x-2x^2),
matrix(1,3,y,""="",-2x^2+8x),
Find,
vertex,
using,
-b/(2a),
for,
x-coordinate,
of,
vertex,
a=-2,
b=8,
-b/(2a)=-8/(2*(-2))=8/4=2,
y-coordinate,
of,
vertex,
is,
y-2(2)^2+8(2)=-2(4)+16=8,
vertex="(2,8)" )}}}  {{{drawing(3200/13,400,-2,6,-3,10,graph(3200/13,400,-2,6,-3,10,-2x^2+8x),
locate(2,8.5,"vertex(2,8)"))}}} {{{matrix(11,1,Answer="",x=2,inches,for,maximum,cross-section,area,of,8,square,inches)}}}

Edwin</pre>