Optimised Understanding Quadratic Functions | Definitions, Applications, and the Quadratic Formula

Quadratic function

A quadratic function is a mathematical function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0

A quadratic function is a mathematical function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0. It represents a second-degree polynomial equation and is a specific type of polynomial function. The graph of a quadratic function is a parabola.

The coefficient “a” determines whether the parabola opens upwards (a > 0) or downwards (a < 0). The term "bx" represents the linear term, and "c" is the constant term. The term "x^2" is the quadratic term, which is the highest power of x in the function. The vertex of a quadratic function is a notable point on its graph. If the quadratic function is in the form f(x) = ax^2 + bx + c, the x-coordinate of the vertex is given by the equation x = -b / (2a). The corresponding y-coordinate can then be found by evaluating f(x) at this x-value. Quadratic functions are widely used in various fields of mathematics and science, such as physics, engineering, economics, and computer science. They are used to model real-world situations and solve problems involving quadratic equations. The quadratic formula, (-b ± √(b^2 - 4ac)) / (2a), is often used to find the roots, or solutions, of quadratic equations.

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