Answer
The equation that corresponds to ${{y}_{1}}$ in the given table is ${{y}_{1}}={{x}^{2}}$.
Thus, option (b) is correct.
Work Step by Step
The option (a) is given as ${{y}_{1}}=-3x$
Now, put the value of x as 1; the value of ${{y}_{1}}$ is $-3$, which does not match the values in the table. So, option (a) is not correct.
The option (c) is given as ${{y}_{1}}=-{{x}^{2}}$.
Now, put the value of x as 1; the value of ${{y}_{1}}$ is $-1$, which does not match the values in the table. So, option (c) is not correct.
The option (d) is given as ${{y}_{1}}=2-x$.
Now, put the value of x as 2; the value of ${{y}_{1}}$ is 0, which does not match the values in the table. So, option (d) is not correct.
The option (b) is given as ${{y}_{1}}={{x}^{2}}$.
Now, put the value of x as 0; the value of ${{y}_{1}}$ is 0, which matches the values in the table. If we check any other value of x and y, results will match. So, option (b) is correct.
Thus, the correct option is b.
