1. Because y=ax2+bx+c is translated from y=-2x2, a=-2, fixed-point coordinate -b/2a=-3, (4ac-b2/4a)=4, b=- 12, and c=22.

So y=-2x2- 12x+22.

2. Let the quadratic parabola be y = a (x+h) 2+k h) 2+k.

Vertex coordinates are -h=2 and k=3.

Let (-1, 0) generation y=a(x-2)2+3 and a=- 1/3.

So y=- 1/3(x-2)2+3.

3. The intersection of parabola and Y axis is (0, c). Let (0, c) generation y=x-2 and c=-2, and the parabola is fixed at (-b/2a, (4ac-b2)/4a), that is, (b, (4-b2)/-2).

So y=-? x2+2x-2

4. Intersecting with the Y axis, x=0, so the intersection point is (0, c).

The distance from the axis of symmetry to the Y axis is -b/2a, and the intersection point is the symmetrical point of the axis of symmetry, with the vertical coordinate unchanged and the horizontal coordinate multiplied by two. Just draw a picture. So it must be (-a, b, c)

Sorry, I didn't check it. Please correct any mistakes.