Question

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

Answer 1

Write f(x)=x^2+x+1 and complete the square:

x^2 + x + 1 = (x^2 + x + 1/4) + 3/4 = (x + 1/2)^2 + 3/4.

So the vertex form is f(x) = (x + 1/2)^2 + 3/4 (vertex at (-1/2, 3/4)).