Cubical Parabolic Hyperbola

$\begin{figure}\begin{center}\BoxedEPSF{CubicalParabolicHyper.epsf}\end{center}\end{figure}$

An equation of the form

$\begin{displaymath} y=ax^3+bx^2+cx+d, \end{displaymath}$

where two of the Roots of the equation coincide (and all three are therefore real), i.e.,

$\displaystyle y$	$\textstyle =$	$\displaystyle a(x-r_1)^2(x-r_2)$
	$\textstyle =$	$\displaystyle a[x^3-(2r_1+r_2)x^2+r_1(r_1+2r_2)x-{r_1}^2r_2].$