Answer
$f(x)=2(x-3)^2+1$
See graph
Work Step by Step
We are given the function:
$f(x)=2x^2-12x+19$
Complete the square:
$f(x)=2(x^2-6x)+19=2(x^2-6x+9)-18+19=2(x-3)^2+1$
We start graphing with the basic function $a(x)=x^2$.
We horizontally shift $a(x)$ by 3 units to the right to get $b(x)=(x-3)^2$.
Then we vertically stretch $b(x)$ by a factor of 2 to get $c(x)=2(x-3)^2$.
Finally we vertically shift $c(x)$ one unit upward to get $f(x)=2(x-3)^2+1$.
We use 3 points: $(2,3),(3,1),(4,3)$
