Correct. $\displaystyle{y}={6}{{x}}^{{2}}-{72}{x}+{220}={6}{\left({{x}}^{{2}}-{12}{x}\right)}+{220}\usepackage{cmbright}\Huge\$ . Completing the square, you found $\displaystyle{y}+{6}{\left({36}\right)}={6}{\left({{x}}^{{2}}-{12}{x}+{36}\right)}+{220}\usepackage{cmbright}\Huge\$ . Factoring the trinomial results in $\displaystyle{y}={6}{{\left({x}-{6}\right)}}^{{2}}+{4}\usepackage{cmbright}\Huge\$ . This gives you the coordinates for the vertex, which are $\displaystyle{\left({6},{4}\right)}\usepackage{cmbright}\Huge\$ .