Quadratic function. Given three points in the plane that have different first coordinates and do not lie on a line, there is exactly one quadratic function f whose graph contains all three points. Jul 18, 2019 · In algebra, quadratic functions are any form of the equation y = ax2 + bx + c, where a is not equal to 0, which can be used to solve complex math equations that attempt to evaluate missing factors in the equation by plotting them on a u-shaped figure called a parabola. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. The applet below illustrates this fact. What is Quadratic Function? A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Quadratic functions are symmetric about a vertical axis of symmetry. Apr 10, 2025 · Learn what a quadratic function is, how to graph and solve it. This means that in all quadratic functions, the highest exponent of x x in a non-zero term is equal to two. If a is negative, the parabola is flipped upside down. In this section, we will investigate quadratic functions, which frequently model problems involving area and projectile motion. Working with quadratic functions can be less complex than working with higher degree functions, so they provide a good opportunity for a detailed study of function behavior. It is also called an "Equation of Degree 2" (because of the "2" on the x) Jul 23, 2025 · Quadratic functions are important in various mathematical fields and real-life applications, particularly because their graphs are parabolas. Quadratic functions follow the standard form: If ax2 is not present, the function will be linear and not quadratic. This beginner guide explains the standard form, vertex, and parabola shape with examples. We'll explore how these functions and the parabolas they produce can be used to solve real-world problems. Quadratic functions make a parabolic U-shape on a graph. They are commonly used in contexts where parabolic shapes and properties are needed. The single defining feature of quadratic functions is that they are of the second order, or of degree two. The name Quadratic comes from "quad" meaning square, because the variable gets squared (like x2). What is Quadratic Function? A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. The graph contains three points and a parabola that goes through all three. . We've seen linear and exponential functions, and now we're ready for quadratic functions. quadratic function: A function of degree two.