<image>In the rectangular coordinate plane, the vertex of the quadratic function graph is A(1, -4), and it passes through point B(3, 0).

(1) Find the analytical expression of the quadratic function;
(2) How many units should the graph of this quadratic function be shifted to the right to make the shifted graph pass through the origin? Also, directly write down the coordinates of the other intersection point of the shifted graph with the x-axis.

