We have to use some common sense here along with the rules of parabolas to make this understandable. We should plot the focus and the directrix line to see what we have so far. If the focus is at (-3, 0), it is ON the x-axis, 3 units from the origin. If the directrix is the line x = 3, it is also 3 units from the origin. The focus and the directrix are both the same number of units from the vertex no matter where they are in the coordinate plane; therefore, our vertex is at the origin, (0, 0). The parabola will always "hug" the focus, so that tells us that this parabola is a sideways-opening parabola, opening to the left, to be exact. The formula for a left-opening parabola is [tex]-(y-k)^2=4p(x-h)[/tex]. Our h and k are both 0 so this is a bit simpler: [tex]-y^2=4p(x)[/tex]. P is defined as the distance from the focus to the vertex which is 3 units, so p = 3, and 4p = 12 (4*3=12). So we fill in accordingly: [tex]-y^2=12x[/tex]. That's your parabola. y^2 because it's opening sideways, negative because it opens to the left.
