Answer
Focus: $\left(0,-1\right)$
Directrix: $y=1$
Axis of symmetry: $y$-axis
Work Step by Step
$\bf{Step\text{ }1}$
Bring the equation in standard form:
$$\begin{align*}
y&=-\dfrac{1}{4}x^2&&\text{Write the original equation.}\\
-4y&=x^2&&\text{Multiply by }-4.
\end{align*}$$
$\bf{Step\text{ }2}$
We identify the focus, directrix and axis of symmetry. The equation has the form $x^2=4py$, where $p=-1$. The $\bf{focus}$ is $(0,p)$ or $\left(0,-1\right)$. The $\bf{directrix}$ is $y=-p$ or $y=1$. Because $x$ is squared, the $\bf{axis\text{ } of\text{ }symmetry}$ is the $y$-axis.
$\bf{Step\text{ }3}$
We $\bf{draw}$ the parabola by making a table of values and plotting points. As $p<0$, the parabola opens downward.
\[ \begin{array}{cccccc}
x &|& \pm 1 &|& \pm 2 &|& \pm 3 &|& \pm4 &|& \pm 5 &|&\\
y &|& -0.25 &|& -1 &|& -2.25 &|& -4 &|& -6.25 &|&\\
\end{array}\]
