Question

Betty and Andrea have been solving systems of equations with one polynomial function of degree two and one linear function. Betty says there must always be two solutions, and Andrea says there will no solution. Using complete sentences, explain how Betty can be correct, how Andrea can be correct, and how they both can be wrong.

Answer 1

A system of equations with one polynomial function of degree two and one linear function will have two solutions when the line intersects the parabola at two points.

A system of equations with one polynomial function of degree two and one linear function will have no solution when the line does not intersects the parabola.

A system of equations with one polynomial function of degree two and one linear function will have one solution when the line intersects the parabola at one point.

Answer 2

This system of equations will have two solutions when there are two points that the line intersects with. It will have no solution when the line does not intersect the parabola. It will have only one solution when the line only intersects at one point. Hope this answers the question.