Answer
\[f\left( x \right)=2{{\left( x-5 \right)}^{2}}+3\]
Work Step by Step
We have the quadratic function in its standard form:
$f\left( x \right)=a{{\left( x-h \right)}^{2}}+k,\,\,\,\,\,\,\,\,a\ne 0$.
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 $x=h$.
The coordinates of the vertex of the parabola are $\left( h,\ k \right)$.
Put $a=2,\ h=5,\ k=3$.
Thus, the function in standard form with shape similar to the given function and vertex at $\left( 5,\ 3 \right)$ is written as
$f\left( x \right)=2{{\left( x-5 \right)}^{2}}+3$.
