Determine Algebraically whether f(x) = 1 + x + x^2 is even, odd, or neither

A function is even if f(x) = f(-x), but for our function

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

so it is not even.

To be odd -f(x)=f(-x), and for our function

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

and so it is also not odd.

Therefore it is neither.