#### Answer

\[f\left( x \right)=2{{\left( x+10 \right)}^{2}}-5\]

#### 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 $x=h$.
The coordinates of the vertex of the parabola is $\left( h,\ k \right)$.
Put $a=2,\ h=-10,\ k=-5.$
Thus, the function in standard form with shape similar to the given function and vertex at $\left( -10,-5 \right)$ is written as
$f\left( x \right)=2{{\left( x+10 \right)}^{2}}-5$.