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.
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.
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