Precalculus (6th Edition) Blitzer

No, the graph of ${{Y}_{2}}$ does not pass through the origin.
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.