Answer
Vertex is (4, -3)
Focus is (3.5, -3)
Directrix is x = 4.5
Work Step by Step
$(y-k)^{2} = 4p(x-h)$
$y^{2} + 6y + 2x + 1 = 0$
$y^{2} + 6y = -2x - 1$
$y^{2} + 6y + 9 = -2x - 1 + 9$
$(y+3)^{2} = -2x +8 $
$(y+3)^{2} = -2(x - 4) $
4p = -2
p = -0.5
Vertex is (h,k), so it is (4, -3)
Focus is (h+p, k) = (4 - 0.5, -3) = (3.5, -3)
Directrix is x = h-p = (4 - (-0.5)) = 4.5
