## Precalculus (6th Edition) Blitzer

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 $\left( 5,-1 \right)$.
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.