Systems — Linear-Quadratic and Quadratic-Quadratic

When a line meets a parabola, there can be 0, 1, or 2 intersection points. These points are the solutions to a linear-quadratic system. Finding them requires substituting the linear equation into the quadratic and solving the resulting quadratic. Two parabolas can intersect in 0, 1, or 2 points as well. The geometry and the algebra tell the same story.