Intersection of a Line and Curve

This activity asks learners to divide a set of 10 cards into four subsets according to the type of intersection of the given curve with the given line. This can be done as a calculator exercise with follow-up work on exact and algebraic solutions, or as an algebra exercise with the calculator being used as a check. The algebra requires solution of quadratic equations, cubic equations with at least one integer root and quartic equations that are quadratic in x².