QUADRATIC FUNCTION Meaning and
Definition
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A quadratic function is a mathematical function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants and x is the variable. The term "quadratic" refers to the fact that the highest power of the variable, x, is squared. It is a specific type of polynomial function and is widely used in various branches of mathematics, including algebra and calculus.
Quadratic functions are characterized by the presence of a degree two polynomial expression. The quadratic term, ax^2, is the primary component of these functions, while bx represents the linear term and c denotes the constant term. The coefficients a, b, and c determine the specific shape and behavior of the quadratic function.
A quadratic function typically outputs a parabolic curve when graphed on a coordinate plane. The vertex of this curve represents the minimum or maximum point of the function, and its position depends on the values of a, b, and c. The axis of symmetry is a vertical line that passes through the vertex, dividing the parabola into two equal halves.
Quadratic functions are widely used in physics, engineering, and other scientific fields to model a variety of phenomena. They can be utilized to represent motion, trajectory, growth, optimization, and many other real-life applications. Moreover, quadratic equations, obtained by setting the quadratic function equal to zero, have valuable applications in solving real-world problems, finding the roots, or determining the solutions of a given equation.
Etymology of QUADRATIC FUNCTION
The term "quadratic" is derived from the Latin word "quadratus", meaning "square" or "square-shaped". In mathematics, a quadratic function is a polynomial function of degree two, meaning it can be written in the form of y = ax^2 + bx + c. The name "quadratic" refers to the fact that the highest power of the variable (x) is squared. So, a quadratic function represents a parabolic shape, which is a particular type of curve.
