Answer
vertex (-0.5,2)
focus (0,2)
directrix x=-1
Work Step by Step
simplify the equation to:
(y-2)^{2}=2(x+\frac{1}{2})
(y-h)^{2}=4p(x-k)
then the vertex is (h,k)=(-0.5,2) from the equation.
from the equation 4p=2 then p=1/2
directrix formula: (x-h)=-p
then (x+0.5)=-0.5
directrix is x=-1
the focus is (p+h,0+k) = (0.5-0.5,2)=(0,2)
