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Cubic Functions

Change the coefficients a, b, c, and d, and watch the function and the roots change.

Brief Explanation

The general cubic expression is written as ax3 + bx2 + cx + d. As you change the coefficients below, the graph redraws itself on the left. If the graph goes through whole-number points, they are highlighted.

The standard cubic equation asks “When is the expression zero?” The roots, on the right, are plotted in the complex plane.


Try It Yourself

 FunctionRoots


y = ∙x3 + ∙x2 + ∙x +

y = 0 where x = + ∙ i
y = 0 where x = + ∙ i
y = 0 where x = + ∙ i



Slide to set a


Slide to set b


Slide to set c


Slide to set d

Remarks

The formula for finding the roots of a cubic equation is considerably more complicated than for quadratics. Either the roots are all real, or one is real and two are complex conjugates.


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