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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.

    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

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