Final answer:
The equation of a parabola with vertex (0,0) and directrix x= -2 is y = 2x^2 or y = -2x^2.
Step-by-step explanation:
The equation of a parabola with vertex (0,0) and directrix x= -2 can be found using the standard form of the equation of a parabola: y = a(x-h)^2 + k, where (h, k) is the vertex.
Since the vertex is (0,0), the equation becomes: y = ax^2.
To find the value of a, we need to use the fact that the distance between the vertex and the directrix is equal to the distance between the vertex and any point on the parabola. In this case, the distance is 2 units, because the directrix is x = -2. Therefore, we have the equation: 2 = |0-a(0)^2|/1 which simplifies to 2 = |0-a|.
Solving for a, we get a = 2 or a = -2. Therefore, the equation of the parabola is either y = 2x^2 or y = -2x^2.