Quadratic functions

A quadratic function is a mathematical expression where the highest power of the variable (usually x) is two, written as \( ax^2 + bx + c \). It often models situations involving acceleration or curved relationships, like the path of a ball in the air. The graph of a quadratic function is a U-shaped curve called a parabola. The position and shape of the parabola depend on the coefficients \( a, b, \) and \( c \). Quadratic functions are useful for analyzing problems involving optimization, motion, and areas, providing insights into maximums, minimums, and symmetry.