Answer
(a)
Vertex: $V(3,-1)$
Focus: $F(3,1)$
Directrix: $y=-3$
(b)
Work Step by Step
Equation of a parabola with vertical axis and vertex at $(h,k)$:
$(x-h)^2=4p(y-k)$
$(x-3)^2=8(y+1)$
$(x-3)^2=8[y-(-1)]$
$h=3$
$k=-1$
Vertex: $V(3,-1)$
$4p=8$
$p=2$. Parabola opens upward.
The given equation can be obtained by shifting
$x^2=8y$
right 3 units and downward 1 unit. In this equation:
Focus: $F(0,p)=F(0,2)$
Directrix: $y=-p=-2$
Now, shift the vertex and the directrix 3 units to the right and 1 unit downward:
Focus: $F(3,1)$
Directrix: $y=-3$
