Answer
The required value is $\left( 3,\ 1 \right)$
Work Step by Step
The quadratic function in its standard form can be written as
$f\left( x \right)=a{{\left( x-h \right)}^{2}}+k,\,\,\,\,\,\,\,\,a\ne 0$
Here, $a,\ h\ ,\ k$ are constants and $x$ is a variable. The graph of $f\left( x \right)$ is a parabola which is symmetric about the line $x=h$.
Now, the coordinates of the vertex of the parabola are $\left( h,\ k \right)$.
Consider the provided function $f\left( x \right)=2{{\left( x-3 \right)}^{2}}+1$. Compare the function with the standard form.
The point $\left( h,\ k \right)$ is $\left( 3,\ 1 \right)$
