Correct. $\displaystyle{y}={4}{{x}}^{{2}}+{24}{x}+{42}={4}{\left({{x}}^{{2}}+{6}{x}\right)}+{42}\usepackage{cmbright}\Huge\$ . Completing the square, you found $\displaystyle{y}+{4}{\left({9}\right)}={4}{\left({{x}}^{{2}}+{6}{x}+{9}\right)}+{42}\usepackage{cmbright}\Huge\$ . Factoring the trinomial results in $\displaystyle{y}={4}{{\left({x}+{3}\right)}}^{{2}}+{6}\usepackage{cmbright}\Huge\$ . This equation is now in vertex form, $\displaystyle{y}={a}{{\left({x}-{h}\right)}}^{{2}}+{k}\usepackage{cmbright}\Huge\$ , and you can find the vertex, $\displaystyle{\left({h},{k}\right)}\usepackage{cmbright}\Huge\$ . The coordinates of the vertex are $\displaystyle{\left(-{3},{6}\right)}\usepackage{cmbright}\Huge\$ .