# How do you identify the vertical asymptotes of f(x) =2/(x^2+3x-10)?

Jul 16, 2015

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.)

#### Explanation:

$f \left(x\right) = \frac{2}{{x}^{2} + 3 x - 10}$

The denominator is $0$ when

${x}^{2} + 3 x - 10 = 0$

$\left(x + 5\right) \left(x - 2\right) = 0$

The zeros are $- 5$ and $2$

(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:

$x = - 5$ and $x = 2$