y+1=(-1/12)(x-3)^2 is the form y-k=a(x-h)^2 in which the vertex (h,k) can be clearly seen as (3,-1). The line of symmetry is x=3, passing through the vertex (maximum) and focus, and the parabola is an inverted broad U shape, because a<0. The curve cuts the y axis (y intercept) when x=0, so y=-1-3/4=-7/4.
The focus is a distance 1/4a below the vertex at (3,-4) and the directrix line, y=2, is the same distance above the vertex at (3,2). The latus rectum is where the line y=-4 cuts the curve: -3=(-1/12)(x-3)^2; 36=(x-3)^2, x-3=+6, x=9, -3 so the end points are (-3,-4) and (9,-4).