In mathematics, a quadratic function of a single variable is a function of the form f ( x ) = a x 2 + b x + c , a ≠ 0 , {\displaystyle f(x)=ax^{2}+bx+c...

solutions of the equation, and roots or zeros of the quadratic function on its left-hand side. A quadratic equation has at most two solutions. If there is...

Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks...

by a quadratic function is called the LQ problem. One of the main results in the theory is that the solution is provided by the linear–quadratic regulator...

algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation. Other ways of solving quadratic equations,...

regression theory, which is based on the quadratic loss function. The quadratic loss function is also used in linear-quadratic optimal control problems. In these...

square-integrable function, also called a quadratically integrable function or L 2 {\displaystyle L^{2}} function or square-summable function, is a real- or...

and statistics, the U-quadratic distribution is a continuous probability distribution defined by a unique convex quadratic function with lower limit a and...

another plane that is tangential to the conical surface. The graph of a quadratic function y = a x 2 + b x + c {\displaystyle y=ax^{2}+bx+c} (with a ≠ 0 {\displaystyle...

quartic function is a cubic function. Sometimes the term biquadratic is used instead of quartic, but, usually, biquadratic function refers to a quadratic function...

Quadratic probing is an open addressing scheme in computer programming for resolving hash collisions in hash tables. Quadratic probing operates by taking...

number), a quadratic function c x 2 {\displaystyle cx^{2}} ( c {\displaystyle c} as a nonnegative real number) and an exponential function c e x {\displaystyle...

quadratically constrained quadratic program (QCQP) is an optimization problem in which both the objective function and the constraints are quadratic functions...

also used for graphing quadratic functions, deriving the quadratic formula, and more generally in computations involving quadratic polynomials, for example...

include constant functions, linear functions and quadratic functions. Rational functions are quotients of two polynomial functions, and their domain...

solutions are called roots of the function. The derivative of a cubic function is a quadratic function. A cubic function with real coefficients has either...

is often useful to specify quadratic degrees of freedom. These are degrees of freedom that contribute in a quadratic function to the energy of the system...

chemistry to form basis sets. Gaussian functions arise by composing the exponential function with a concave quadratic function: f ( x ) = exp ⁡ ( α x 2 + β x...

difficult than regular linear programming. Quadratic programming allows the objective function to have quadratic terms, while the feasible set must be specified...

for square. Quadratic function (or quadratic polynomial), a polynomial function that contains terms of at most second degree Complex quadratic polynomials...

+Y_{m}^{2}\right)/m}}\sim F_{n,m}.} A quadratic form of a normal vector, i.e. a quadratic function q = ∑ x i 2 + ∑ x j + c {\textstyle q=\sum x_{i}^{2}+\sum...

function. The dot product of a Euclidean vector with itself is equal to the square of its length: v⋅v = v2. This is further generalised to quadratic forms...

associated with a quadratic equation; it is named after Thomas Carlyle. The circle has the property that the solutions of the quadratic equation are the...

generalizes the conjugate gradient method to nonlinear optimization. For a quadratic function f ( x ) {\displaystyle \displaystyle f(x)} f ( x ) = ‖ A x − b ‖ 2...

constructing Lyapunov functions for ODEs, in many specific cases the construction of Lyapunov functions is known. For instance, quadratic functions suffice for...

theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime...

known as quadratic functions or specially multiplicative functions. Euler's function φ ( n ) {\displaystyle \varphi (n)} is a totient function, and the...

straight line. Quadratic function: Second degree polynomial, graph is a parabola. Cubic function: Third degree polynomial. Quartic function: Fourth degree...

theory, a quadratic field is an algebraic number field of degree two over Q {\displaystyle \mathbf {Q} } , the rational numbers. Every such quadratic field...

logarithm of earnings is modelled as the sum of years of education and a quadratic function of "years of potential experience". ln ⁡ w = f ( s , x ) = ln ⁡ w...