Second-Power Equations

A quadratic equation has a variable raised to the second power: ax² + bx + c = 0. The equation x² = 4 is quadratic. So is 2x² − 5x + 3 = 0. The defining feature is the x² term — which is what turns flat lines into curves and makes the math richer than anything in linear algebra.

Every quadratic traces out a parabola when graphed — a U-shaped curve. That single shape describes a thrown ball's flight, the bowl of a satellite dish, the cables on a suspension bridge, and the focusing surface of a car headlight. One equation, one shape, a thousand applications.