Activity Overview
In this Derive™ activity, students understand how the software solves cubic equations and relate it to contributions made by del Ferro, Tartaglia, and Cardan in finding the method of solving cubic equations.
Before the Activity
See the attached DFW file for detailed instructions for this activity
Print pages from the attached DFW file for your class
During the Activity
Distribute the pages to the class.
Follow the Activity Procedures:
Set up a 2D plot window
Enter the standard cubic equation and choose random values for its coefficients
Continue simplifying until values obtained for the variable, coeff, contains all non zero values
Define a function and expand it so that the function is seen as a cubic
Adjust the scale and plot a graph that includes both the maximum and minimum values of the function
Shift the axes, and eliminate the squared term in the cubic equation by making a substitution for x in terms of another variable
Expand the result in terms of the new variable
Find the value which causes the coefficient of the squared term to be zero
Substitute the value in the expression and observe that the resulting cubic in the new variable has no squared term
Substitute the new variable with yet another quantity
Simplify the expression, work backwards, and determine the value of x
By factoring, find all the values of x that satisfy the standard cubic expression
After the Activity
Students answer questions listed on the activity sheet.
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary