The given point is (3,6), and the vertex is (1,2). This means
[tex]\begin{gathered} x=3,y=6 \\ h=1,k=2 \end{gathered}[/tex]
We use the vertex form of a quadratic function.
[tex]y=a(x-h)^2+k[/tex]
Let's replace the given values to find a.
[tex]\begin{gathered} 6=a(3-1)^2+2 \\ 6=a(2)^2+2 \\ 6-2=4a \\ a=\frac{4}{4}=1 \end{gathered}[/tex]
Once we have a, we can write the function using the vertex-form and the vertex point.
[tex]y=a(x-h)^2+k[/tex]
Hence, the function is
[tex]f(x)=(x-1)^2+2[/tex]
