Activity Overview
In this Computer Algebra System (CAS) activity, students use CAS to prove a theorem regarding cubic functions, their zeros [roots], and tangents to the curves.
Before the Activity
Install TI Connect™ using the TI connectivity cableSee the attached PDF file for detailed instructions for this activity Print the attached PDF file for the class
During the Activity
Distribute the page to the class.
Follow the Activity procedures:
Graph a cubic function and find its roots
Graph the tangent line at the average of two of these roots
Determine the root of the tangent line
Graph the tangent line at the average of two roots [different from the roots used earlier]
Observe that in each case, the tangent line at the average of two of the roots appears to go through the other root of the cubic function
Repeat the steps with other third degree polynomials
Check if the pattern continues
Make a conjecture and prove it using CAS on the calculator
After the Activity
Students' answer questions on the Activity sheet.
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary