This topic examines the properties of quadratic function, Pythagorean theorem and the knowledge of solving side length by using the properties of right triangle. This question is a bit difficult, but it is much easier if there are hints between questions. The answer is/exercise/math /799455/? I hope you can adopt the exam. Ask me if you don't understand. Have a nice summer vacation.

Quadratic function y = a (the square of x -2mx-3m) (where a and m are constants and a >；; 0, m>0) intersects the X axis at point A and point B (point A is on the left of point B), and intersects the Y axis at point C (0, -3). Point D is on the image of quadratic function, CD//AB is connected with AD, and ray AE intersects with quadratic function through the bisecting angle DAE of point A at points E and AB.

(2) Verification: AD/AE is a fixed value;

(3) Let the vertex of the quadratic function image be F, and explore whether there is a point G on the negative semi-axis of the X axis, which connects GF, and the triangle with the lengths of the line segments GF, AD and AE as three sides is a right triangle. if