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.

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step-by-step explanation: