Activity Overview
This Computer Algebra System (CAS) activity encourages students to investigate numerical and graphical properties of cubic functions, and to verify the results using CAS.
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:
Enter a cubic function and graph it
Draw a tangent at a point on the curve, and find the point at which the tangent line intersects the curve
Explore the relationship between the x-coordinates of the two points, between the slopes of the curve at those points, and between the y-intercepts of the tangent lines at those points
Graph a cubic function and understand that it is symmetric to its point of inflection
Find the coordinates of the inflection point
Translate the function so that the inflection point is at the origin
Establish that symmetry exists by proving the translated function is odd
Consider a cubic polynomial function with three distinct real zeros
Find the point where the tangent line drawn to the curve at the average of two of the three zeros intersects the curve
Decide if this property holds, irrespective of the averaged zeros
Find if this property is true for cubic functions with only one or two distinct zeros
Graph a cubic function and determine the point where the tangent intersects the curve
Divide this region into two parts
Find the ratio of the areas of the two regions
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