If you want to have an exact method to find the end behavior of a function, you need to use limits, which are introduced in pre-calculus. Namely, the limit as x approaches infinity or negative infinity for this function is 1/3.
Edit: the response above mine is wrong, as it is clearly possible to factor 12x^2 + x - 1 into (4x - 1)(3x + 1). Furthermore, even if it were impossible to factor the quadratic polynomial, that does not mean it has no roots, you would have to use the quadratic formula. If and only if the discriminant of the quadratic formula (which is b^2 - 4ac) is less than 0, the polynomial is said to have no real roots. If the discrminiant is not negative, then the polynomial has either 1 root (when the discrminiant is equal to 0) or two roots (when the discriminant is positive). If the discriminant is positive but not a perfect square, then the roots do exist, but they are just not rational numbers.