This problem is a comprehensive test of quadratic function. This paper probes into how to determine the intersection point of parabola and axis by using the root of quadratic equation of one variable, how to find the analytical formula of linear function by using undetermined coefficient method, the judgment and properties of congruent triangles, and the properties of right triangle. It is the key to solve the analytical formula by the method of undetermined coefficients, and it is the key and difficult point to flexibly use the properties of right triangle in solving.

Solution: (1) makes y = 0, x 2-2mx+m 2-9 = 0, so △ = (-2m) 2-4m 2+36 >: 0, so whatever the value of m is, the equation x 2-2mx+m 2-.

(1) Verification: No matter what the value of m is, there are always two intersections between parabola and X axis;

(2) The parabola intersects the X axis at points A and B, and point A is on the left side of point B, OA.

(3) Under the condition of 2, the intersection of parabola symmetry axis and X axis is n, if point M is any point on line AN, the intersection point M is a straight line MC perpendicular to X axis, parabola intersects with point C, the symmetrical point of point C about parabola symmetry axis is d, and point P is a point on line MC, and it satisfies MP= 1/4MC, connecting CD and PD so that PE is perpendicular to PD and X axis.