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