The given equation is written as
(y - 1)2 = -4(x + 1/2)
Let X = x + 1/2 and Y = y -1
Then we have
Y2 = -4X
Therefore, the vertex is given by
(X = 0,Y = 0) = (-1/2, 1)
Since a = 1, the focus (X = −1, Y = 0) is
X = a or x + 1/2 = 1 or x - 1/2 = 0
The latus rectum is given by 4a = 4