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 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:

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