Find the vertex focus and directrix of the following parabol

Find the vertex, focus, and directrix of the following parabola. Graph the equation Verify your graph using a graphing utility. (y + 2)^2 = 12(x + 4) The vertex of the parabola is.

Solution

(y+2)²=12(x+4)

(1/12)(y+2)²-4=x

center=(-2,-4)

focus=(h + (1/4a),k) =( -2 + (1/48),-4) =(-95/48,-4)

directrix

x=h-(1/4a) = -2-(1/48)=-97/48