Find the maximum area of a triangle underneath a parabola

Question

An Isosceles triangle ABC is embedded in the parabola y=x(4-x). C is always at the point (2,0) while A and B are at the same but variable height above the x-axis. Find the maximum area of ABC.

I figured out that the equation for the triangle would be A=h(2-z), z being an unknown variable, but I'm not sure how to put it in terms of x and then differentiate

Answer 1

A(.67, 2.22), B(2.33, 2.22) or more precisely A(2/3, 20/9) and B(10/3, 20/9) or (2/3, 2 2/9) & (3 8/3, 2 2/9)

with C(2,0) form the inscribed triangle

with Area =bh/2 = (4/3)(20/9)/2 = 80/27 = about 3.36 square units