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

See also Cubical Conic Section, Cubical Ellipse, Cubical Hyperbola, Cubical Parabola, Hyperbola




© 1996-9 Eric W. Weisstein
1999-05-25