Education Technology

Intersection of a Line with a Parabola

Published on 07/30/2005

Activity Overview

In this activity, students use Computer Algebra System (CAS) tools to find intersections of linear and non-linear equations. They confirm their answers by graphing the equations on the calculator.

Before the Activity

  • Download TI Connect™ using the TI Connectivity Cable
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 1 - 14 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Evaluate the discriminant for the equation of parabola and decide how many solutions are possible
  • Equate the equations for the line and the parabola and find the values of x and y
  • Determine the point(s) of intersection
  • Alternatively, graph the line and the parabola on the calculator, and determine the point(s) of intersection
  • Else, tabulate results for different values of x for each equation, sketch both graphs on the same set of axes, and mark the point(s) of intersection
  • Repeat the procedure with different sets of lines and parabolas
  • Summarize the findings and understand how the value of the discriminant indicates the number of intersection points
  • Repeat the steps to determine intersection points between a line and a circle, and a line and a rectangular hyperbola
  • After the Activity

    Students prepare a general case for the intersection between a line and a conic section.

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary