A quadratic expression is a type of polynomial expression that has the general form ax^2 + bx + c, where a, b, and c are constants, and x represents a variable. The term ax^2 indicates that the highest power of the variable is 2, which gives the expression its "quadratic" name. Quadratic expressions can represent various real-world situations, such as projectile motion or area calculations. Quadratic expressions can be factored, graphed, or solved using methods like completing the square or the quadratic formula, x = (-b ± √(b^2 - 4ac)) / 2a. The graph of a quadratic expression is a parabola, which can open upwards or downwards depending on the sign of a. Understanding quadratic expressions is essential in algebra and higher mathematics.