When you put this into standard form for a parabola, your equation (after much sweating and bleeding from the eyeballs) found by completing the square is:
, which has a vertex at (-2.4, 7.6). To find the distance that the directrix is from the vertex (which is also the same distance the focus is from the vertex) we use the fact that
(you can omit the negative in front of it cuz distance will always be positive), and
. Since this is an upside down parabola, the focus is under the vertex ("inside" the parabola) while the directrix is above it. The directrix is a horizontal line. Because it is a horizontal line, it is 5/32 above the y-coordinate (or k) or the vertex. So we add 5/32 to the y-coordinate of the vertex to get 7.6+5/32 and that gives us a directrix of y = 7.76 rounded.