f(x)=2x²-12x+19=2(x²-6x+9-9)+19,
f(x)=2(x-3)²-18+19=2(x-3)²+1 has a vertex at (3,1).
On the left side of the vertex f(x) is decreasing and on the right side it’s increasing. That is, x<3 decreasing, x>3 increasing; or (-∞,3) decreasing, (3,∞) increasing.