Which is the equation of a parabola with Vertex (0, 0) and directrix x = - 2

The equation would be: y^2=8x

The directrix line located at x=-2 which makes a vertical line. The location of the directrix is at the left of the vertex. This means the parabola would be opened up to the right.

Then, the parabola graph equation would be: y^2 = ax+b. The graph has vertex in (0,0) so we can conclude that b=0 by putting the value to the equation.

y^2 = ax+b

0^2 = a (0) + b

b=0

If you mirroring the line from the directrix to the vertex, you can get that the focus coordinate is 2,0 which makes the distance to focus is 2 (p=2)

Using focus equation you can get:

(y-k) ^2 = 4p (x-h)

(y-0) ^2=4 (2) (x-0)

y^2 = 8x