Find min or max value

Question

f(x)=x^2+x+1

Answer 1

There is no max; the min is at the vertex, where x = -b/(2a).

Answer 2

Or you can put this in vertex form.

 

f(x) = x² + x + (1/4) - (1/4) + 1

 

f(x) = (x - 1/2)² + (3/4)

 

 

Minimum is (1/2, 3/4)