(1)∫ The image of inverse proportional function y=kx and the image of quadratic function y=ax2+x- 1 intersect at point A (2,2).

∴k=4,a= 14，

∴ The analytical formula of inverse proportional function is: y = 4x,

The analytical formula of quadratic function is: y = 14x2+x? 1;

(2)∫ quadratic function y = 14x2+x? The vertex of the image of 1 is B(-2, -2),

In y=4x, when x=-2, y = 4? 2=? 2,

∴ Vertex B(-2, -2) is on the image of inverse proportional function;

(3)∵ Point P is on the image with y = 4x, and the abscissa of point P is 1.

∴P( 1,4)，

∴s△aop= 1×4+ 12(2+4)×(2- 1)- 12× 1×4- 12×2×2，

=4+3-2-2,

=3.