#### Answer

B

#### Work Step by Step

We know that the equation of $y=x^{2}$ is a parabola that opens upwards with its vertex at the origin.
Upon observation, we see that the graph in the question is essentially the same as the graph of $y=x^{2}$ except that it has its vertex at $y=2$. This means that the graph of $y=x^{2}$ has been moved two units upwards.
According to the rule of vertical translations, if the graph of $y=f(x)$ is shifted by $c$ units upwards,its equation becomes $y=f(x)+c$. This means that the equation for the graph in the question is $y=x^{2}+2$.
As a result, the equation $y=x^{2}+2$ is matched with option B.