Answer
The statement, “The vertex of the parabola described by $f\left( x \right)=2{{\left( x-5 \right)}^{2}}-1$ is at $\left( 5,1 \right).$ ” is False. The vertex is at $\left( 5,-1 \right)$.
Work Step by Step
The general form of a parabola is defined as $f\left( x \right)={{\left( x-h \right)}^{2}}+k$.
Where, $a\ne 0$ and $\left( h,k \right)$ is the vertex of the parabola.
Hence, compare the provided equation with the general form of a parabola and get,
$h=5$ and $k=-1$.
Thus, the vertex is $\left( 5,-1 \right)$.
Therefore, the provided statement is false.
