Final answer:
The equation of the parabola with a vertex at (0,0) and a focus at (-2,0) is ² = -8, reflecting the fact that the parabola opens to the left.
Step-by-step explanation:
To find the equation of a parabola with a vertex at (0,0) and a focus at (-2,0), we can use the standard form of a parabola's equation which is either y2 = 4px for a horizontal parabola or x2 = 4py for a vertical parabola. In this case, since the focus is on the x-axis and to the left of the vertex, the parabola opens to the left, which means it's a horizontal parabola.
The distance between the vertex and focus, p, is 2 (as the focus is at -2,0). Therefore, the value of p is -2 (negative because the parabola opens to the left). Substituting p into the standard form gives us y2 = -8x. This is the equation of the parabola that satisfies the given conditions.