Answer
Focus: $\left(-\frac{3}{2},0\right)$
Directrix: $x=\frac{3}{2}$
Axis of symmetry: $x$-axis
Work Step by Step
$\bf{Step\text{ }1}$
The equation is in standard form:
$$y^2=-6x.$$
$\bf{Step\text{ }2}$
We identify the focus, directrix and axis of symmetry. The equation has the form $y^2=4px$, where $p=-\frac{3}{2}$. The $\bf{focus}$ is $(p,0)$ or $\left(-\frac{3}{2},0\right)$. The $\bf{directrix}$ is $x=-p$ or $x=\frac{3}{2}$. Because $y$ is squared, the $\bf{axis\text{ } of\text{ }symmetry}$ is the $x$-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 to the left. So we will use only negative $x$-values.
\[ \begin{array}{cccccc}
x &|& -1 &|& -2 &|& -3 &|& -4 &|& -5 &|&\\
y &|& \pm 2.49 &|& \pm 3.46 &|& \pm 4.24 &|& \pm 4.90 &|& \pm5.48 &|&\\
\end{array}\]
