Activity Overview
This activity illustrates how to use the Computer Algebra System CAS tool to graph and analyze parabolas.
Before the Activity
See the attached PDF file for detailed instructions for this activity
Print pages 1 - 3 from the attached PDF file for the class
During the Activity
Distribute the pages to the class.
Follow the Activity procedures:
Plot the graph of a polynomial
Calculate the slope of the line which passes through two points on the graph
Find the first derivative and illustrate the result graphically
Repeat the steps for other polynomials and different points
Prove the standard derivative formula using various polynomials
Determine the coordinates of the summit of a given parabola
Find the equation of the tangent at a given point
Determine the coordinates of the point of intersection of the tangent and the axis of the parabola
Make a conjecture for the ordinates of the summit point, tangential point, and the point of intersection
Find the abscissa of the point of intersection between the tangent lines at any two points on the parabola
Calculate the area defined by the parabola, the tangents, and the vertical line
Prove that the vertical line divides the region between the parabola and the tangents into two regions with equal areas
After the Activity
Students complete the exercises listed on the activity pages.
Review student results.
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary