Given quadratic equation ,

\(\displaystyle{y}={6}{\left({x}-{2}\right)}^{{2}}+{10}\)

On simplifying,

\(\displaystyle{y}={6}{\left({x}^{{2}}+{4}-{4}{x}\right)}+{10}\)

\(\displaystyle{y}={6}{x}^{{2}}-{24}{x}+{24}+{10}\) (1)

\(\displaystyle{y}={6}{x}^{{2}}-{24}{x}+{34}\)

Now, this equation compare with general quadratic equation,

\(\displaystyle{a}{x}^{{2}}+{b}{x}+{c}\)

a = 6 , b = -24 , c = 34

\(\displaystyle{h}=-\frac{{b}}{{2}}{a}\)

\(\displaystyle=-\frac{{-{24}}}{{{2}\cdot{6}}}\)

= 2

Now putting x= 2 in equation (i), then we get

\(\displaystyle{y}={6}\cdot{2}^{{2}}-{24}\cdot{2}+{34}\)

y = 24 - 48 + 34

y = 10

(2, 10) is the vertex of given quadratic equation.

\(\displaystyle{y}={6}{\left({x}-{2}\right)}^{{2}}+{10}\)

On simplifying,

\(\displaystyle{y}={6}{\left({x}^{{2}}+{4}-{4}{x}\right)}+{10}\)

\(\displaystyle{y}={6}{x}^{{2}}-{24}{x}+{24}+{10}\) (1)

\(\displaystyle{y}={6}{x}^{{2}}-{24}{x}+{34}\)

Now, this equation compare with general quadratic equation,

\(\displaystyle{a}{x}^{{2}}+{b}{x}+{c}\)

a = 6 , b = -24 , c = 34

\(\displaystyle{h}=-\frac{{b}}{{2}}{a}\)

\(\displaystyle=-\frac{{-{24}}}{{{2}\cdot{6}}}\)

= 2

Now putting x= 2 in equation (i), then we get

\(\displaystyle{y}={6}\cdot{2}^{{2}}-{24}\cdot{2}+{34}\)

y = 24 - 48 + 34

y = 10

(2, 10) is the vertex of given quadratic equation.