Find the horizontal and vertical asymptotes of the curve. y = 3x2 + x − 9 x2 + x − 72

The horizontal asymptotes rely on the degree of the numerator and the degree of the denominator.  Since our degrees are the same then the hor. asymptote is equal to the leading coefficients in fraction form or 3/1 or just 3.  For the vertical asymptote, factor the denominator and see what you get.  When you factor that out you get that x = 8 and x = -9, or (x - 8)(x + 9).  Therefore, our vertical asymptotes are at x = 8 and x = -9.