Find the horizontal and vertical asymptote(s) of $LaTeX: \displaystyle f(x) = \frac{x^{2} + 2 x - 80}{2 x^{2} + 12 x + 10}$ , if they exist.

The degree of the numerator is the same as the degree of the denominator, so the horizontal asymptote is the ratio of the leading coefficients $LaTeX: \displaystyle y=\frac{1}{2}$ . The vertical asymptotes are the zeros of the denominator. $LaTeX: \displaystyle 2 x^{2} + 12 x + 10=0 \iff 2 \left(x + 1\right) \left(x + 5\right)=0$ . The vertical asymptotes are $LaTeX: \displaystyle x=-5$ and $LaTeX: \displaystyle x=-1$ .