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