1. **State the problem:** We are given a parabola with vertex $V(0,1)$ and directrix $x = -2$. We need to find the equation of this parabola. 2. **Recall the definition and formula:** A parabola is the set of points equidistant from the vertex (focus) and the directrix line. The vertex form of a parabola that opens horizontally 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 (and also to the directrix). 3. **Identify the orientation:** Since the directrix is a vertical line $x = -2$ and the vertex is at $(0,1)$, the parabola opens horizontally. 4. **Calculate $p$:** The vertex is at $x=0$ and the directrix is at $x=-2$, so the distance between them is $$ |0 - (-2)| = 2 $$ Since the vertex is midway between the focus and directrix, the focus is at $$ x = 0 + 2 = 2 $$ and $p = 2$. 5. **Write the equation:** Using vertex $(h,k) = (0,1)$ and $p=2$, the equation is $$ (y - 1)^2 = 4 \times 2 \times (x - 0) $$ which simplifies to $$ (y - 1)^2 = 8x $$ 6. **Interpretation:** This is the equation of the parabola with vertex at $(0,1)$ and directrix $x = -2$ opening to the right. **Final answer:** $$ (y - 1)^2 = 8x $$