Solution: Let parabola y=2X? -12X+ 16 rotates 180 degrees around its vertex, but the opening direction of the parabola is changed, and the opening size, symmetry axis and vertex are unchanged.

y=2X？ - 12X+ 16=2(x-3)^2-2，

So after rotation, it is y =-2 (x-3) 2-2 =-2x2+12x-16.

So the analytical formula of parabola is y =-2x 2+ 12x-20.