Answer
The parabola, the focus and the directrix should be rotated by $180$ degrees.
Work Step by Step
$\bf{Step\text{ }1}$
Bring the equation in standard form:
$$\begin{align*}
0.5y^2+x&=0&&\text{Write the original equation.}\\
0.5y^2&=-x&&\text{Subtract }x\text { from reach side.}\\
y^2&=-2x&&\text{Multiply both sides by }2.
\end{align*}$$
$\bf{Step\text{ }2}$
We identify the focus, directrix and axis of symmetry. The equation has the form $y^2=4px$, where $p=-0.5$. The $\bf{focus}$ is $(p,0)$ or $\left(-0.5,0\right)$. The $\bf{directrix}$ is $x=-p$ or $x=0.5$. 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.
\[ \begin{array}{cccccc}
x &|& -1 &|& -2 &|& -3 &|& -4 &|& -5 &|&\\
y &|& \pm 1.41 &|& \pm 2 &|& \pm 2.45 &|& \pm 2.83 &|& \pm 3.16 &|&\\
\end{array}\]
The mistake in the given graph is that the parabola, the focus and the directrix should be rotated by $180$ degrees.
Here is the correct graph:
