Linear–Quadratic Systems

The Desmos trick

Graph the line and the parabola together. Click each intersection point. If the line just grazes the curve (tangent), there's exactly one point — Desmos shows it clearly even when the algebra (discriminant = 0) is easy to miss.

• Graph both expressions on separate lines in the same calculator
• Click every visible intersection — don't assume there's only one
• If you see no crossing, zoom out before concluding there's no solution