Answer:
C
Step-by-step explanation:
Given
f(x) = x² + x + 1
To express in vertex form use the method of completing the square
add/subtract ( half the coefficient of the x- term)² to x² + 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
