Answer
$2(x-3)^2+1$
See graph.
Work Step by Step
Step 1. $f(x)=2x^2-12x+19=2(x^2-6x++9)-18+19=2(x-3)^2+1$
Step 2. To graph $f(x)$, start with $y=x^2$, shift $3$ units to the right, stretch vertically by a factor of 2, then shift $1$ unit up. See graph.