To find the equation of a parabola through the vertices of the group of parabolas, , we choose 3 values for b and find the vertex for each parabola.

So, if , the vertex will be

And if , the vertex will be

And if , the vertex will be

Substituting these points into , we get the system of equations below.

These equations simplify to,

When we solve the system, we find that a = -1, b = 0, and c = 1.

So, the equation of the desired parabola is,