calculus help me

Question

Find the minimal value of the function f(x)=|x²+x+1|+x+2

Answer 1

Since x² + x + 1 > 0 for all x, the absolute value signs are superfluous.

f(x) = x² + x + 1 + x + 2

f(x) = x² + 2x + 3

Use completion of the square to put into vertex form and determine minimum.