Final answer:
The equation of the parabola with vertex (0, 0) and directrix x = 2 is x² = -8y, which is derived from the general form of the parabola equation using the vertex and the distance to the focus.
Step-by-step explanation:
To find the equation of a parabola with vertex at (0, 0) and directrix x = 2, we use the fact that the distance from any point P(x, y) on the parabola to the focus is the same as the distance from P to the directrix. Since the vertex is at the origin and the directrix is a vertical line, the focus would be at (-2, 0). The general form of the equation of a parabola is (x - h)² = 4p(y - k), where (h, k) is the vertex of the parabola and p is the distance between the vertex and the focus.
In this case, since the vertex is (0, 0) and the focus is at (-2, 0), p is -2 (p is negative because the parabola opens to the left). Therefore, we have x² = -8y. This is the equation of our parabola.