Answer
\[f\left( x \right)=2{{\left( x-7 \right)}^{2}}+4\].
Work Step by Step
We know that 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 $x=h$.
And the coordinates of the vertex of the parabola are $\left( h,\ k \right)$.
Substitute $a=2,\ h=7,\ k=4$
Thus, the function in standard form with shape similar to the given function and vertex at $\left( 7,\ 4 \right)$ is written as
$f\left( x \right)=2{{\left( x-7 \right)}^{2}}+4$.
