The function image passes through the symmetry point (4,0) about x=2.

So let y=ax(x-4)

y=a(x-2)^2-4a

Because there is a maximum value of 2.

Open down

A "0"

When x=2, take the maximum value -4a=2.

So a=- 1/2.

therefore

Analytical formula y =-x 2/2+2x