The problem presents the equation $x^2 = -12y$. We need to find the form of this equation. It looks like a parabola.

1. Problem Description

The problem presents the equation $x^2 = -12y$. We need to find the form of this equation. It looks like a parabola.

2. Solution Steps

The equation is given as $x^2 = -12y$.

We can rewrite this as $x^2 = 4(-3)y$.

The general form of a parabola opening upward or downward with vertex at the origin is $x^2 = 4py$, where $p$ is the distance from the vertex to the focus and from the vertex to the directrix.

In this case, we have $4p = -12$, which gives $p = -3$. Since $p$ is negative, the parabola opens downward.

The vertex is at $(0, 0)$.

The focus is at $(0, p)$, so the focus is at $(0, -3)$.

The directrix is $y = -p$, so the directrix is $y = 3$.

3. Final Answer

The equation represents a parabola opening downward with vertex at the origin. The equation can be written as $x^2 = -12y$.