From the information given in the statement, you can see that the original function, before the transformation, is
![g(x)=x^2](https://img.qammunity.org/2023/formulas/mathematics/high-school/l8iqt2sov300tbb361hkpjcfi5j75gwcao.png)
Now, by the rules of transformation of functions you know that:
*g(x - h) moves the function g(x) h units right
*g(x) + k moves the function g(x) k units up
So, in this case, you have
![\begin{gathered} f(x)=(x-3)^2+5 \\ h=3 \\ k=5 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/h3cjnwwcx3jjqx1tj7wsz1ef5ordrtzdos.png)
Which implies that the original graph will move 3 units to the right and 5 units up.
Therefore, the graph that represents the given quadratic function is the graph of option B.