Verified answer

x^2+6x+y-12=0

y=-x^2-6x+12

x^2+6x +9= -y +12+9 (completion of squares by adding 9 to both sides)

(x+3)^2= -y+21 so -(y-21) >vertex(-3,+21) open down now to find focus 4c=-1(coeffient of right side) c=-1/4

focus(-3-1/4,+21)=(-13/4,+21)

direcrix equation X=-3 +1/4=-11/4