Answer
Vertex = $(0,0)$;
Focus = $\left(0, -\dfrac{1}{16}\right)$;
Directrix $y=\dfrac{1}{16}$;
Axis of symmetry $x=0$.
Work Step by Step
We are given that $x^2=-\dfrac{1}{4} y$
This equation has the form as $x^2 =4py$ wherein $4p=-\frac{1}{4} \implies p=-\dfrac{1}{16}$
Here, the vertex is $(0,0)$ and the axis of symmetry is the y-axis, that is, $x=0$
and the x-term is squared which shows that the parabola is vertical with focus $(0,p)=\left(0, -\dfrac{1}{16}\right)$.
Now, the directrix is $y=-p=-\left(-\dfrac{1}{16}\right)=\dfrac{1}{16}$
Our results are:
Vertex = $(0,0)$;
Focus = $\left(0, -\dfrac{1}{16}\right)$;
Directrix $y=\dfrac{1}{16}$;
Axis of symmetry $x=0$.
