Question 960100
Information for better guidance:


x-intercepts are the same as ROOTS or ZEROS for the function, which appear in the numerator.  Think, "binomial factors".


Horizontal asymptote means that the degree of numerator and denominator are equal.


You correctly chose degree two for numerator and denominator.  The horizontal asymptote means that the leading terms of numerator and denominator become increasingly important as x goes to the left or the right unbounded, and the ratio of their coefficients will approach  {{{1/2}}}.


That should be enough to make the proper adjustments.  You almost have it.