Education Technology

Cubic, Zeros and Tangents

Published on 06/09/2008

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 cable
  • See 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