Answer
$f(x)=2(x-3)^2+1$
Work Step by Step
Completing the square:
$f(x)=2x^2-12x+19$
$f(x)=2(x^2-6x)+19$
$f(x)=2(x^2-6x+(\frac{6}{2})^2)-2\cdot(\frac{6}{2})^2+19$
$f(x)=2(x^2-6x+3^2)-2\cdot3^2+19$
$f(x)=2(x-3)^2-18+19$
$f(x)=2(x-3)^2+1$
Graphing the function:
1st step (black graph): The parent function: $y=x^2$
2nd step (green graph): Stretch by a factor of 2. $y=2x^2$
3rd set (red graph): Shift 1 unit up. $y=2x^2+1$
Final step (blue graph): Shift right by 3 units. $y=2(x-3)^2+1$
