# Activities

• ##### Download

• • ##### Subject Area

• Math: Algebra I: Linear Functions
• Math: Algebra I: Quadratic Functions

• ##### Author 9-12

60 Minutes

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

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Report an Issue

Intersection of a Line with a Parabola

#### 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