quadratic model - meaning and definition. What is quadratic model
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  3. quadratic model

What (who) is quadratic model - definition

POLYNOMIAL EQUATION IN A SINGLE VARIABLE WHERE THE HIGHEST EXPONENT OF THE VARIABLE IS 2
Quadratic equations; Quadratic Equation; The Quadratic Equation; Quadratic model; Bhaskarachārya's Formula; Bhaskaracharya's Formula; ABC formula; Quadform; Quadratic solution formula; Quadratic Factoring Formula; Ax2+bx+c; Ax^2+bx+c; Ax2 + bx + c; Ax² + bx + c; Second degree equation; Second-degree equation; Ax^2+bx+c=0; Ax2+bx+c=0; Factoring a quadratic expression; Solving quadratic equations
  • Carlyle circle of the quadratic equation ''x''<sup>2</sup>&nbsp;&minus;&nbsp;''sx''&nbsp;+&nbsp;''p''&nbsp;=&nbsp;0.
  • ''x''<sup>2</sup> + ''bx'' + ''c'' {{=}} 0}} compared with the value calculated using the quadratic formula
  • ''xc''}} is 0.732050807569, accurate to twelve significant figures.
  • a}} value should be considered negative here, as its direction (downwards) is opposite to the height measurement (upwards).
  • alt=Figure 6. Geometric solution of eh x squared plus b x plus c = 0 using Lill's method. The geometric construction is as follows: Draw a trapezoid S Eh B C. Line S Eh of length eh is the vertical left side of the trapezoid. Line Eh B of length b is the horizontal bottom of the trapezoid. Line B C of length c is the vertical right side of the trapezoid. Line C S completes the trapezoid. From the midpoint of line C S, draw a circle passing through points C and S. Depending on the relative lengths of eh, b, and c, the circle may or may not intersect line Eh B. If it does, then the equation has a solution. If we call the intersection points X 1 and X 2, then the two solutions are given by negative Eh X 1 divided by S Eh, and negative Eh X 2 divided by S Eh.
  • alt=Figure 2 illustrates an x y plot of the quadratic function f of x equals x squared minus x minus 2. The x-coordinate of the points where the graph intersects the x-axis, x equals &minus;1 and x equals 2, are the solutions of the quadratic equation x squared minus x minus 2 equals zero.
  • ''x''}}-axis at all.
  • <!-- Note: The unusual spellings in this alt text (for example, "eh" for the constant "a" ) is intended to aid enunciation by screen readers. Before changing any alt text, please test your changes in multiple screen readers. -->alt=Figure 1. Plots of the quadratic function, y = eh x squared plus b x plus c, varying each coefficient separately while the other coefficients are fixed at values eh = 1, b = 0, c = 0. The left plot illustrates varying c. When c equals 0, the vertex of the parabola representing the quadratic function is centered on the origin, and the parabola rises on both sides of the origin, opening to the top. When c is greater than zero, the parabola does not change in shape, but its vertex is raised above the origin. When c is less than zero, the vertex of the parabola is lowered below the origin. The center plot illustrates varying b. When b is less than zero, the parabola representing the quadratic function is unchanged in shape, but its vertex is shifted to the right of and below the origin. When b is greater than zero, its vertex is shifted to the left of and below the origin. The vertices of the family of curves created by varying b follow along a parabolic curve. The right plot illustrates varying eh. When eh is positive, the quadratic function is a parabola opening to the top. When eh is zero, the quadratic function is a horizontal straight line. When eh is negative, the quadratic function is a parabola opening to the bottom.

Quadratic irrational number         
MATHEMATICAL CONCEPT
Quadratic surd; Quadratic irrationality; Quadratic Irrational Number; Quadratic irrationalities; Quadratic irrational; Quadratic irrational numbers
In mathematics, a quadratic irrational number (also known as a quadratic irrational, a quadratic irrationality or quadratic surd) is an irrational number that is the solution to some quadratic equation with rational coefficients which is irreducible over the rational numbers.Jörn Steuding, Diophantine Analysis, (2005), Chapman & Hall, p.
https://en.wikipedia.org/wiki/Quadratic_irrational_number
Quadratic reciprocity         
THEOREM
Law of quadratic reciprocity; Quadratic reciprocity rule; Aureum Theorema; Law of Quadratic Reciprocity; Quadratic reciprocity law; Quadratic reciprocity theorem; Quadratic Reciprocity; Qr theorem
In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. Due to its subtlety, it has many formulations, but the most standard statement is:
https://en.wikipedia.org/wiki/Quadratic_reciprocity
Linear–quadratic regulator         
LINEAR OPTIMAL CONTROL TECHNIQUE
Linear-quadratic control; Dynamic Riccati equation; Linear-quadratic regulator; Quadratic quadratic regulator; Quadratic–quadratic regulator; Quadratic-quadratic regulator; Polynomial quadratic regulator; Polynomial–quadratic regulator; Polynomial-quadratic regulator; Linear quadratic regulator
The theory of optimal control is concerned with operating a dynamic system at minimum cost. The case where the system dynamics are described by a set of linear differential equations and the cost is described by a quadratic function is called the LQ problem.
https://en.wikipedia.org/wiki/Linear–quadratic_regulator

Wikipedia

Quadratic equation

In algebra, a quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as

where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.) The numbers a, b, and c are the coefficients of the equation and may be distinguished by respectively calling them, the quadratic coefficient, the linear coefficient and the constant coefficient or free term.

The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two complex solutions that are complex conjugates of each other. A quadratic equation always has two roots, if complex roots are included; and a double root is counted for two. A quadratic equation can be factored into an equivalent equation

where r and s are the solutions for x.

The quadratic formula

expresses the solutions in terms of a, b, and c. Completing the square is one of several ways for deriving the formula.

Solutions to problems that can be expressed in terms of quadratic equations were known as early as 2000 BC.

Because the quadratic equation involves only one unknown, it is called "univariate". The quadratic equation contains only powers of x that are non-negative integers, and therefore it is a polynomial equation. In particular, it is a second-degree polynomial equation, since the greatest power is two.

https://en.wikipedia.org/wiki/Quadratic equation
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