And x= 1 is the symmetry axis of the function image,

Therefore, the length of the line segment cut from its image on the X axis is 8, and its two intersections with the X axis are (-3,0), (5,0),

Namely 9a-3b+c=0, 25a+5b+c=0,

A=- 1，b=2，c= 15，

Therefore, y =-x 2+2x+ 15.

2) Translate the point (2,0) by 5 units to the right, and then translate 1 unit to get (7, 1).

So the vertex of the parabola is (7, 1).

Let y = a (x-7) 2+ 1, and a (1-7) 2+ 1 = 0 from a+b+c=0, so a=- 1/36,

So y =-1/36 * (x-7) 2+1=-1/36 * x 2+7/18 * x-13/36,

Then a=- 1/36, b=7/ 18 and c=- 13/36.