Answer:
C
Step-by-step explanation:
Given
f(x) = x² + x + 1
To obtain the function in vertex form use the method of completing the square.
Add/ subtract ( half the coefficient of the x- term )² to x² + x
f(x) = x² + 2([tex]\frac{1}{2}[/tex] )x + [tex]\frac{1}{4}[/tex] - [tex]\frac{1}{4}[/tex] + 1
= (x + [tex]\frac{1}{2}[/tex] )² + [tex]\frac{3}{4}[/tex] → C
