# How do you find the asymptotes for y = (8 x^2 + x - 2)/(x^2 + x - 72)?

Mar 11, 2016

Vertical asymptotes: $x = - 8 , x = 9$
Horizontal asymptote: $y = 8$

#### Explanation:

To find the vertical asymptotes of a rational equation, find when the equation's denominator equals $0$:

${x}^{2} - x - 72 = 0$

$\left(x - 9\right) \left(x + 8\right) = 0$

$x = 9 , x = - 8$

These are where vertical asymptotes will occur.

As for horizontal asymptotes, examine the degree of the numerator and denominator. They are both $2$. When the numerator and denominator of a rational function have the same degree, the horizontal asymptote can be found by dividing the two terms with the largest degree:

$\frac{8 {x}^{2}}{x} ^ 2 = 8$

Thus there is a horizontal asymptote at $y = 8$.

We can check a graph:

graph{(8 x^2 + x - 2)/(x^2 + x - 72) [-13, 12, -50, 50]}