I think you are talking about quadratic inequalities right? If it just has one intercept that means the it will always be positive or zero or always be negative or zero. So your solution interval intervals will reflect that.
Some examples x^2 > 0 (- ∞ , 0) U (0, ∞) and. x^2 ≥ 0 has (- ∞ , ∞) , x^2 < 0 the solution set is empty.
Since quadratics with one solution are essentially horizontal translations of this graph the form (x ± k)^2 can you finish it from there?