Oxford University MAT 2018 Solved Papers

We can complete the square for $\mathit{f}\left(\mathit{x}\right)={\left(\mathit{x}-\frac{5}{2}\right)}^2+\frac{3}{4}$. This has a minimum at $\left(\frac{5}{2},\frac{3}{4}\right)$. Then the graph of $\mathit{f}\left(\mathit{x}-2\right)$ is a translation of the graph of $\mathit{f}\left(\mathit{x}\right)$ by two in the positive $\mathit{x}$-direction. So the minimum is translated to $\left(\frac{9}{2},\frac{3}{4}\right)$. The answer is (b).