Ok, if the vertex of a parabola is (-1, -1), then its equation should be y = (x+1)2-1. Since xy = 1, y = 1/x. Equate the two equations to get 1/x = x2+2x, which can be rearranged to x2+2x- (1/x) = 0. Multiply both sides by x to give x3+2x2-1 = 0.
Now, since x = -1 is a root of this equation...