What type of function is x² + 2x + 1 ?

The story behind the answer

Quadratic is correct because the highest power of x is 2. The expression fits the standard form ax² + bx + c with a = 1, b = 2, c = 1. In fact, x² + 2x + 1 factors to (x + 1)², showing it’s a perfect square. Its graph is a parabola opening upward with vertex at (−1, 0) and a single real root (discriminant b² − 4ac = 0).

Tip to remember: if there’s an x² term and no higher power, it’s quadratic. “Quadratic” comes from “quadratus,” Latin for “square,” which connects to both the squared term and the solving method “completing the square.” Quadratics model parabolic motion, areas, and many optimization problems.