Answer
No, the graph of ${{Y}_{2}}$ does not pass through the origin.
Work Step by Step
The table shows different values x for different values of y.
The provided table represents the value of ${{y}_{2}}=0$ when $x=2$.
For the graph to be passing through the origin, the equation of the graph must have passed through $\left( 0,0 \right)$.
Therefore, according to the given table, the graph does not pass through the origin.