Answer:
The vertex is ( -1/2, 3/4)
Step-by-step explanation:
f(x)=x^2+x+1
The vertex form is
y = a( x-h) ^2 +k where (h,k) is the vertex
Rewriting the function by completing the square
Taking the coefficient of x and dividing by 2 and squaring it
(1/2) ^2 = 1/4
Adding it and subtracting it
f(x) = x^2 + x + 1/4 -1/4 +1
= ( x^2+ x +1/4) + 3/4
= ( x+ 1/2) ^2 + 3/4
= ( x- -1/2) ^2 + 3/4
The vertex is ( -1/2, 3/4)
