Answer
See image
Work Step by Step
Write $f$ in the form $f(x)=a(x-h)^{2}+k$:
$\begin{aligned}f(x)&=2x^{2}-4x+1\\&=2\left(x^{2}-2x\right)+1\\&=2\left(x^{2}-2x+1\right)+1-2\\&=2(x-1)^{2}-1\end{aligned}$
Let $f_{1}(x)=x^{2}$.
Then, $f(x)=2f_{1}(x-1)-1$.
The graph is obtained from $f_{1}(x)$ by
- vertical stretching by factor $2,$
- shifting to the right by 1 unit,
- and then down by 1 unit
Point by point,
$\left[\begin{array}{lllll}
(x,y) & \rightarrow & (x,2y) & \rightarrow & (x+1,2y-1)\\
& & & & \\
(0,0) & \rightarrow & (0,0) & \rightarrow & (1,-1)\\
(-1,1) & \rightarrow & (-1,2) & \rightarrow & (0,1)\\
(1,1) & \rightarrow & (1,2) & \rightarrow & (2,1)\\
(-2,4) & \rightarrow & (-2,8) & \rightarrow & (-1,7)\\
(2,4) & \rightarrow & (2,8) & \rightarrow & (3,7)
\end{array}\right]$
