1. **State the problem:** We are given a parabola with vertex at $(-4,-2)$ and a point on the parabola at $(-1,4)$. The parabola opens to the right. We want to find the equation of this parabola. 2. **Formula and explanation:** For a parabola that opens horizontally (to the right or left), the standard form is: $$ (y-k)^2 = 4p(x-h) $$ where $(h,k)$ is the vertex and $p$ is the distance from the vertex to the focus. If $p>0$, the parabola opens to the right; if $p<0$, it opens to the left. 3. **Substitute the vertex:** Here, $h = -4$ and $k = -2$, so the equation becomes: $$ (y + 2)^2 = 4p(x + 4) $$ 4. **Use the given point to find $p$:** The point $(-1,4)$ lies on the parabola, so substitute $x = -1$ and $y = 4$: $$ (4 + 2)^2 = 4p(-1 + 4) $$ $$ 6^2 = 4p(3) $$ $$ 36 = 12p $$ 5. **Solve for $p$:** $$ p = \frac{36}{12} = 3 $$ 6. **Write the final equation:** $$ (y + 2)^2 = 12(x + 4) $$ This is the equation of the parabola that opens to the right with vertex $(-4,-2)$ passing through $(-1,4)$.