Topic: Grand finale; Classified discussion.

Analysis: (1) According to the coordinate characteristics of points on the X axis and Y axis, the coordinates of points A, B and D can be obtained;

(2) The undetermined coefficient method firstly obtains the analytical expression of straight line ed, and then obtains the positional relationship between straight line and circle according to the judgment of tangent;

(3) When 0 < m < 3 and m > 3, the function about m is obtained through discussion.

Solution: (1) A (-m, 0), B(3m, 0), D(0, (root number 3) m).

(2) Let the analytical formula of straight line ED be y=kx+b, and substitute E (-3,0) and D (0 0,m) to obtain:

Solution, k= root number 3/3, b= root number 3m.

The analytical formula of straight line ED is y= root number 3/3 mx+ root number 3m.

Turn y =- root 3/3m (x+m) (x-3m) into a vertex: y =- root 3/3m (x+m) 2+m. 。

∴ The coordinate of the vertex m is (m, the root of (4) 3/3 m). Substitute y= root number 3/3 mx+ root number 3m, m2 = m.

∵ m > 0，∴ m= 1。 So when m = 1, the point m is on the straight line DE.

Connect CD, C is the midpoint of AB, and the coordinate of point C is C(m, 0).

Od =, OC= 1, ∴CD=2, and point D is on the circle.

OE=3，DE2=OD2+OE2= 12，

ec2= 16,cd2=4,∴cd2+de2=ec2.

∴∠FDC=90

The straight line ED is tangent to C.

(3) when 0 < m < 3, s △ aed = AE. OD= m(3﹣m)

S=﹣ m2+ m

When m > 3, s △ aed = 1/2ae. OD= root number 3/2m (m ~ 3).

That is, S= root number 3/2m2_ 3 root number 3/2m.

Comments: This topic is called Quadratic Function Synthesis, and the knowledge points involved are the coordinate characteristics of points on X axis and Y axis, the determination of parabola analytical formula, the vertex formula of parabola and the solution of triangle area. Pay attention to the discussion results of the problem.

It's exhausting to give points.