Key Idea: One Solution (Quadratic System)

A quadratic system has one real solution when the quadratic and the line (or another curve) touch at exactly one point — typically where the line is tangent to the parabola.

General Rule:

• Use the discriminant:

• If Δ=0, there is exactly one real solution.

Why this matters for the SAT:

The discriminant gives a quick way to determine how many solutions a quadratic system has without solving. A discriminant of zero indicates one point of intersection, often signaling a tangent line.