Step-by-step explanation:
A line and a quadratic (parabola) can have either 0, 1, or 2 solutions.
- 0 solutions: the line and quadratic do not intersect.
- 1 solution: the line and quadratic are tangent (intersect at one point), or the line is the axis of symmetry (intersects only at the vertex).
- 2 solutions: the line and quadratic intersect at two points.
It is impossible for a linear-quadratic system to have more than 2 solutions.
