Answer
Vertex = $(0,0)$;
Focus = $\left(0, -\dfrac{9}{4}\right)$;
Directrix $y=\dfrac{9}{4}$;
Axis of symmetry $x=0$.
Work Step by Step
We are given that $x^2=-9y$
This equation has the form as $x^2 =4py$ wherein $4p=-9 \implies p=-\dfrac{9}{4}$
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 $(0,p)=\left(0, -\dfrac{9}{4}\right)$.
Now, the directrix is $y=-p=-\left(-\dfrac{9}{4}\right)=\dfrac{9}{4}$
Our results are:
Vertex = $(0,0)$;
Focus = $\left(0, -\dfrac{9}{4}\right)$;
Directrix $y=\dfrac{9}{4}$;
Axis of symmetry $x=0$.
