The representation of a quadratic eqauation in vertex form is
[tex]y=a(x-k)^2+h[/tex]The given vertex is,
[tex](k,h)=(-2,4)[/tex]And the given point through which the graph passes is,
[tex](x,y)=(3,6)[/tex]Substitute the values in the formula of quadratic equation.
[tex]\begin{gathered} 6=a(3-(-2))+4 \\ 6=a(3+2)+4 \\ 6=5a+4 \\ 5a=6-4 \\ 5a=2 \\ a=\frac{5}{2} \end{gathered}[/tex]Hence, the equation in vertex form will be,
[tex]\begin{gathered} y=\frac{5}{2}(x-(-2))+4 \\ y=\frac{5}{2}(x+2)+4 \end{gathered}[/tex]