You probably recognized that the graph is a parabola, so you chose a quadratic function with the correct vertex, $\displaystyle{\left({0},{1}\right)}\usepackage{cmbright}\Huge\$ . However, the graph of $\displaystyle{f{{\left({x}\right)}}}=\frac{{1}}{{2}}{{x}}^{{2}}+{1}\usepackage{cmbright}\Huge\$ also contains the points $\displaystyle{\left(-{2},{3}\right)}\usepackage{cmbright}\Huge\$ and $\displaystyle{\left({2},{3}\right)}\usepackage{cmbright}\Huge\$ , for example, and these are not on the given graph.