Answer
Vertex: $(0,0)$
Focus: $\left(2,0\right)$
Directrix: $x=-2$
See graph
Work Step by Step
We are given the parabola:
$y^2=8x$
The standard equation is:
$(y-k)^2=4p(x-h)$
Determine $h,k,p$:
$h=0$
$k=0$
$4p=8\Rightarrow p=2$
Determine the vertex:
$(h,k)=(0,0)$
Determine the focus:
$(h+p,k)=\left(0+2,0\right)=\left(2,0\right)$
Determine the directrix:
$x=h-p$
$x=0-2$
$x=-2$
Determine the two points defining the latus rectum:
$x=2$
$y^2=4(2)(2)$
$y^2=16$
$y=\pm 4$
$\Rightarrow (2,-4),(2,4)$
Plot the points, draw the directrix, and graph the parabola:
