Education Technology

Nonlinear Systems of Equations

Activity Overview

Students will be introduced to nonlinear systems of equations. It begins by allowing students to move figures around the screen to see ways certain types of graphs (linear/conic and conic/conic) can intersect each other and how many possible intersection points are possible. The activity concludes by having students look at the equations in a nonlinear system, stating how many solutions are possible, and then solving the system by graphing.

Key Steps

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    In problem 1, students explore the number of possible intersection points when using nonlinear system of equations. They move a circle and observe how many ways a line intersects it.

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    They move onto a hyperbola and an ellipse to find the number of possible intersection points.
    Students may conjecture that for the graphs of a linear and quadratic function, there are either 0, 1, or 2 points of intersection.

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    Students will look at intersections of a pair of graphs of quadratic functions. Students will see a circle and hyperbola with no intersection points. Here, they animate point A and watch the circle move across the screen. Students will see the circle intersect the hyperbola at 2, 3, and 4 places.