Correct. $\displaystyle{y}={6}{{x}}^{{2}}-{24}{x}+{15}={6}{\left({{x}}^{{2}}-{4}{x}\right)}+{15}\usepackage{cmbright}\Huge\$ . Completing the square, you found $\displaystyle{y}+{6}{\left({4}\right)}={6}{\left({{x}}^{{2}}-{4}{x}+{4}\right)}+{15}\usepackage{cmbright}\Huge\$ . Factoring the trinomial results in $\displaystyle{y}={6}{{\left({x}-{2}\right)}}^{{2}}-{9}\usepackage{cmbright}\Huge\$ . Note that the coordinates for the vertex would be (2, -9).