Solution: (1) Let y= 1/2x- 1=0 respectively, and get x=2, that is, A (2 2,0); Substituting x=-8 into y= 1/2x- 1, we can know B(-8,-5); Substituting these two coordinates into y =- 1/4x 2+bx+c gives-1/4*2? +2b+c=0，- 1/4(-8)？ -8b+c=-5, simultaneous solution, b=- 1, c=3. So the analytical formula of this parabola is y=- 1/4x? -x+3 .

(2)∫△PAB happens to be a right triangle, and P is a point on a parabola.

∴ Only ∠ APB = 90, that is, AP⊥PB.

∴ The product of the slopes of the straight line AP and the straight line PB is equal to-1.

Let P(x,-1/4x 2-x+3), with a coordinate of (2,0) and b coordinate of (-8,5).

∴[(- 1/4x^2-x+3)/(x-2)]*[(- 1/4x^2-x+3+5)/(x+8)]=- 1

That is, (x+6)(x-4)=- 16, and the solution is x=2 (discarded) or x=-4.

The point p that satisfies the condition is (-4,3).