Cubical Parabola

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

An equation of the form

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

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

$\begin{displaymath} y=a(x-r)^3=a(x^3-3rx^2-3r^2x-r^3). \end{displaymath}$