Answer
See graphs
Work Step by Step
We are given the function:
$f(x)=2x^2-4x+1$
Rewrite the function building the square:
$f(x)=2(x^2-2x+1)-2+1=2(x-1)^2-1$
We start by graphing the parent function $a(x)=x^2$.
Then horizontally shift $a(x)$ one unit to the right to get $b(x)=(x-1)^2$.
Then vertically stretch $b(x)$ by a factor of 2 to get $c(x)=2(x-1)^2$.
Finally, vertically shift $c(x)$ one unit downward to get $f(x)=2(x-1)^2-1$.
