Answer
Vertex: : $(3,-1)$
Focus: $(7,-1)$
Directrix: $x=-1$
Work Step by Step
Recall: The parabola $(y-b)^2=4p(x-a)$ has a vertex $(a,b)$, a focus $(a+p,b)$, and a directrix $x=-p+a$.
We have $(y+1)^2=16(x-3)$ or equivalently $(y-(-1))^2=16(x-3)$.
Then,
$(a,b)=(3,-1)$
$4p=16$
$p=\frac{16}{4}$
$p=4$
So, the vertex is $(3,-1)$, the focus is $(7,-1)$, and the directrix is $x=-1$.
Sketch the graph: