In problem 1, students explore the number of possible intersection points when using nonlinear system of equations. They begin by graphing a circle (shown to the right), a horizontal and vertical line.

Students move on to a parabola and investigate its possible intersection points. Students will see that for graphs of a linear and quadratic function, there are either 0, 1, or 2 points of intersection.

Students continue to problem 1 by investigating an ellipse and a hyperbola.

Students use the graphs of a hyperbola and two circles to determine the number of intersection points. They will see that the inside circle is a circle with radius one and has no points of intersection. The larger circle has four points of intersection.