Answer
The graph is shown below,
Work Step by Step
The coefficient of ${{x}^{2}}$ is not 1.
Factor out 2 from the first two terms.
Therefore, $f\left( x \right)=2\left( {{x}^{2}}-6x \right)+23$
Complete the square by taking half the coefficient of $x$, squaring it, and subtracting it inside the parentheses.
$\begin{align}
& f\left( x \right)=2\left( {{x}^{2}}-6x+9-9 \right)+23 \\
& =2\left( {{x}^{2}}-6x+9 \right)-\left( 2\cdot 9 \right)+23 \\
& =2\left( {{x}^{2}}-6x+9 \right)-18+23 \\
& =2{{\left( x-3 \right)}^{2}}+5
\end{align}$
Choose some $x$ values, and compute the respective $y$ values.
$x$, $f\left( x \right)=2{{\left( x-3 \right)}^{2}}+5$
$1$, $13$
$2$, $7$
$3$, $5$
$4$, $7$
$5$, $13$
Plot the above points and draw a smooth curve through the points.