To write the standard form of the equation for the parabola, we can use the following information:
- The vertex of the parabola is at \((-3, 1)\).
- The focus of the parabola is at \((-1, 1)\), which means the parabola opens to the right.
The standard form for a horizontally opening parabola is given by:
\[ (y - k)^2 = 4p(x - h) \]
where \((h, k)\) is the vertex and \(p\) is the distance from the vertex to the focus.
In this case:
- The vertex \((h, k) = (-3, 1)\)
- The focus is \((-1, 1)\), so the distance \(p\) from the vertex to the focus is \(2\) (since \(-1 - (-3) = 2\)).
Thus, \(4p = 4 \cdot 2 = 8\).
Now we can substitute the vertex coordinates and the value of \(4p\) into the standard form:
\[ (y - 1)^2 = 8(x + 3) \]
Therefore, the correct equation of the parabola is:
\[ \boxed{(y - 1)^2 = 8(x + 3)} \]