How do you identify the vertical asymptotes of #f(x) =2/(x^2+3x-10)#?
Find the zeros of the denominator and make sure they are not also zeros of the numerator. (If any of them are: factor, reduce the quotient and try again.)
The denominator is
The zeros are
(For a quadratic equation, I always try factoring first, because it's fast. But don't spend a lot of time on factoring, because you can use the quadratic formula to get zeros.)
Obviously, neither of these numbers is a zero of the numerator so:
The vertical asymptotes are the lines whose equations are: