Answer
Vertex: $(0,0)$
Focus: $\left(-4,0\right)$
Directrix: $x=4$
See graph
Work Step by Step
We are given the parabola:
$y^2=-16x$
The standard equation is:
$(y-k)^2=4p(x-h)$
Determine $h,k,p$:
$h=0$
$k=0$
$4p=-16\Rightarrow p=-4$
Determine the vertex:
$(h,k)=(0,0)$
Determine the focus:
$(h+p,k)=\left(0+(-4),0\right)=\left(-4,0\right)$
Determine the directrix:
$x=h-p$
$x=0-(-4)$
$x=4$
Determine the two points defining the latus rectum:
$x=-4$
$y^2=4(-4)(-4)$
$y^2=64$
$y=\pm 8$
$\Rightarrow (-4,-8),(-4,8)$
Plot the points, draw the directrix, and graph the parabola:
