The vertex of this parabola is at (-1,-3) which of the following could be its equation

Since these are parabolas with y being squared, the standard form of such a parabola with vertex at (h, k) is

x = a (y - k) ^2 + h

There are no steps. Just look at what is inside the parentheses and compare it to (y - k) with k = - 3.

Then look at what is added and compare it to h = - 1.

For instance, A has (y + 1) in parentheses. So k = - 1. And it has - 3 added, so h = - 3. That would be a vertex at (-3, - 1).

For

y=a (x-h) ^2+k

vertex is (h, k)

it could be

y=a (x+1) ^2-3