Description: A quadratic function is a polynomial function of degree two typically represented in standard form as f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0. This function has a graph in the shape of a parabola, which can open upwards or downwards depending on the sign of the coefficient ‘a’. Quadratic functions are fundamental in mathematics and have unique properties, such as the existence of a vertex, which represents the maximum or minimum point of the parabola, and symmetry about a vertical line passing through the vertex. In the context of optimization, quadratic functions are used to model nonlinear relationships and to find optimal solutions in minimization or maximization problems. These functions can be applied in various fields, such as computer science and engineering, where they are used to fit curves and surfaces to data, enabling efficient analysis and solutions to real-world problems. The versatility of quadratic functions makes them essential tools in many disciplines, including physics and economics, where they are used to model phenomena that follow quadratic patterns.
