Question 604104
6y = (x + 2)^2 + 6


y = (1/6)(x + 2)^2 + 1 ___ this is the vertex form, with vertex at (-2,1)


the vertex is midway between the focus and the directrix; with the vertex and focus located on the axis of symmetry,
and the directrix perpendicular to it


the distance (p) from the the vertex to the focus (or the directrix) is │1 / 4a│
___ in this case, 6/4 or 3/2


you can think of the focus as being "inside" the curvature of the parabola, while the directrix is "outside"


with this upward opening parabola (a is positive), the focus is above the vertex and the directrix is below it


so the focus is (-2,5/2); and the directrix is y = -1/2