Education Technology

# Activities

• ##### Subject Area

• Math: Calculus: Applications of the Derivative
• Math: Calculus: Series and Taylor Polynomials

9-12

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium
• TI-92 Plus / Voyage™ 200

## Parabolas

#### 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.

• 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