Horizontal asymptotes at:
\( \displaystyle y = \frac{\beta_2}{\beta_4} \)
and vertical asymptotes at:
\( \displaystyle x = \frac{-\beta_3 \pm \sqrt{\beta_3^2 - 4\beta_4}} {2\beta_4} \)
There will be 0, 1, or 2 real solutions to this equation
corresponding to whether
\( \displaystyle \beta_3^2 - 4\beta_4 \)
is negative, zero, or positive.
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