Answer
Focus: $(0,-\frac{1}{16})$ (Red point)
Directrix: $y=\frac{1}{16}$ (Black line)
Work Step by Step
Parabola in the standard form with the vertex at origin (vertical axis):
$x^2=4py$
$y=-4x^2$
$x^2=-\frac{1}{4}y$
That is:
$4py=-\frac{1}{4}y$
$p=-\frac{1}{16}$
$(0,p)=(0,-\frac{1}{16})$
Directrix: $y=-p=\frac{1}{16}$
