Which function in vertex from is equivalent to f(x)=x2+x+1

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)