Answer
(a)
Vertex: $V(3,-1)$
Focus: $F(7,-1)$
Directrix: $x=-1$
(b)
Work Step by Step
Equation of a parabola with horizontal axis and vertex at $(h,k)$:
$(y-k)^2=4p(x-h)$
$(y+1)^2=16(x-3)$
$[y-(-1)]^2=16(x-3)$
$h=3$
$k=-1$
Vertex: $V(3,-1)$
$4p=16$
$p=4$. Parabola opens to the right.
The given equation can be obtained by shifting
$y^2=16x$
right 3 units and downward 1 unit. In this equation:
Focus: $F(p,0)=F(4,0)$
Directrix: $x=-p=-4$
Now, shift the vertex and the directrix 3 units to the right and 1 unit downward:
Focus: $F(7,-1)$
Directrix: $x=-1$
