PreCalculus
Activity:
Nonlinear Systems of Equations
Posted on May 12, 2008
Topic: Conics
In this activity, students see the many ways that certain types of graphs (linear/quadratic and quadratic/quadratic) can intersect each other and how many potential intersection points are possible. Then students look at the equations in a nonlinear system, state how many solutions are possible, and solve the system by graphing.
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Activity Key Steps:
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.
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.
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.
In problem 2, students explore the number of intersections point of two parabolas. Problem 3 will give students the opportunity to investigate solving nonlinear systems by graphing.
At the end of this activity, students will be able to determine the number of possible intersection points when using nonlinear system of equations. They will also be able to solve nonlinear systems of equations by graphing.