Final answer:
The equation of the directrix for a parabola with a vertex at the origin can be found by using the equation x = -p, where p is a constant. We can solve for p using the given information and then substitute it into the equation to find the directrix.
Step-by-step explanation:
The equation of a parabola with a vertex as the origin is y^2 = -4px. To find the equation of the directrix, we need to find the value of p. Given that 4p = 12, we can solve for p by dividing both sides of the equation by 4. This gives us p = 3.
The equation of a directrix for a parabola with a vertex at the origin is x = -p. Substituting the value of p we found (p = 3), we get x = -3 as the equation of the directrix.