What is the minimum value of $f(x) = 2x^2 - 8x + 11$?

Explanation

1. 01

   Complete the square: $2x^2 - 8x + 11 = 2(x - 2)^2 + 3$.

2. 02

   $2(x - 2)^2 \ge 0$, and it is 0 at $x = 2$, so the minimum value is 3.