When y=0 and -3x+3=0, x= 1,
Then the coordinate of point A is (1, 0);
When x=0 and y=3,
Then the coordinate of point C is (0,3);
The symmetry axis of parabola is the straight line x=- 1,
Then the coordinate of point B is (-3,0);
Substituting c (0 0,3) into y=a(x- 1)(x+3) gives 3=-3a.
The solution is a=- 1,
Then the analytical formula of this parabola is y =-(x-1) (x+3) =-x2-2x+3;
(2) The symmetrical point of point A about the straight line L is point B (-3,0).
As shown in figure 1, BC is connected, and the intersection axis is at point p, then the circumference of △PAC is the smallest at this time.
Let the relationship of BC line be: y=mx+n,
Substitute b (-3,0) and c (0 0,3) into y=mx+n? 3m+n=0n=3，
The solution is m = 1n = 3,
The relation of line bC is y=x+3,
When x=- 1 and y=- 1+3=2,
∴ The coordinate of point P is (-1, 2);
3)① When AB is diagonal, as shown in Figure 2,
∵ Quadrilateral AMBN is a parallelogram,
The abscissa of point A is 1, the abscissa of point N is 0 and the abscissa of point B is -3.
The abscissa of point ∴M is -2,
The ordinate of point ∴M is y=-4+4+3=3,
∴M point coordinates are (-2,3);
② When AB is an edge, as shown in Figure 3,
∵ Quadrilateral ABMN is a parallelogram,
∴MN=AB=4, that is, M 1N 1=4, M2N2=4,
The abscissa of ∴m 1 is -4, and the abscissa of M2 is 4.
For y=-x2-2x+3,
When x=-4, y =-16+8+3 =-5;
When x=4, y=- 16-8+3=-2 1,
The coordinates of the point ∴M are (-4, -5) or (4, -2 1).
To sum up, the coordinates of point M are (-2,3) or (-4,5) or (4,21). Take it.