Answer
Zeros are $x=5$ with multiplicity 1 and $x=-4$ with multiplicity 2. At $x=5$ , the graph will cross the $x\text{-axis}$ and at $x=-4$ , the graph will touch the $x\text{-axis}$ and turn around.
Work Step by Step
For zeros:
Let $f\left( x \right)=0$.
$\begin{align}
& 2\left( x-5 \right){{\left( x+4 \right)}^{2}}=0 \\
& \left( x-5 \right){{\left( x+4 \right)}^{2}}=0.
\end{align}$
$x=5,-4$.
For multiplicity:
$x=5$, with a multiplicity 1, because of $\left( x-5 \right)$.
$x=-4$, with a multiplicity 2, because of ${{\left( x+4 \right)}^{2}}$.
The multiplicity of $x=5$ is odd and the graph will cross the $x\text{-axis}$.
The multiplicity of $x=-4$ is even, the graph will touch the $x\text{-axis}$ and turn around.
