What is the equation of a parabola with a vertex at (-2, 0) and a directrix x = - 4.

Step-by-step explanation:

This is a horizontal parabola opening to the right, with vertex at (-2,0) and directrix at x = - 4 (which is to the left of the vertex). The general equation of such a parabola is 4p (x-h) = (y-k) ^2, where p is the number of horizontal units between directrix and vertex; here this quantity is 2.

Substituting known values into the general equation, we get:

4 (2) (x+2) = (y-0) ^2, or 8 (x+2) = y^2.

Check: does (-2,0) satisfy the above equation (as it must) ? 8 (-2+2) = 0^2 YES.