
	Where results make sense

Topic: Quadratic

In the News (Sun 27 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	101 uses of a quadratic equation
		The quadratic equation was held aloft to the nation as an example of the cruel torture inflicted by mathematicians on poor unsuspecting school children.
		Concerned lest dangerous admissions by the quadratic equation remain unchallenged, the vital importance of the equation to the survival of the UK was debated (a positive view was taken, you may be glad to know) in the British House of Commons.
		In fact, the quadratic equation has played a pivotal part in not only the whole of human civilisation as we know it, but in the possible detection of other alien civilisations and even such vital modern activities as watching satellite television.
	plus.maths.org /issue29/features/quadratic/index-gifd.html (0 words)

	SparkNotes: Quadratics: The Quadratic Formula
		Thus, we need a different way to solve quadratic equations.
		Herein lies the importance of the quadratic formula:
		As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b
	www.sparknotes.com /math/algebra1/quadratics/section3.rhtml (264 words)

	Quadratic Functions(General Form)
		Quadratic functions and the properties of their graphs such as vertex and x and y intercepts are explored interactively using applets.
		The x and y coordinates of the vertex are given by h and k respectively.
		The y intercept of the graph of a quadratic function is given by f(0) = c.
	www.analyzemath.com /quadraticg/quadraticg.htm (1425 words)

	PlanetMath: quadratic form
		The definition of equivalent quadratic forms is well-defined and it is not hard to see that this equivalence is an equivalence relation.
		The definiteness of a quadratic form is preserved under the equivalence relation on quadratic forms.
		This is version 39 of quadratic form, born on 2002-02-13, modified 2007-04-15.
	planetmath.org /encyclopedia/QuadraticForm.html (364 words)

	Insights Into Algebra 1 . Workshop 4
		Quadratic functions describe the relationship between height (from the ground) and time (in seconds) of a ball as it bounces.
		A quadratic function is a function f whose value f(x) at x is given by a quadratic polynomial.
		Because the standard and vertex forms of a quadratic function reveal different pieces of information, it is important for students to recognize both and be able to convert one to the other.
	www.learner.org /channel/workshops/algebra/workshop4/index.html (1213 words)

	Quadratic equations - A complete course in algebra
		A QUADRATIC is a polynomial whose highest exponent is 2.
		Therefore, −4 and 2 are the roots of that quadratic.
		A quadratic will have a double root if the quadratic is a perfect square trinomial.
	www.themathpage.com /alg/quadratic-equations.htm (333 words)

	Quadratic Regression and Its Calculus
		Quadratic regression models are often used in economics areas such as utility function, forecasting, cost-befit analysis, etc. This JavaScript provides parabola regression model.
		Thus at X = 2, the slope of the quadratic function is 18(2)- 50 = -14.
		A quadratic is a curve of the parabola family.
	home.ubalt.edu /ntsbarsh/Business-stat/otherapplets/QuadReg.htm (1024 words)

	Reciprocity Laws. Rule of Quadratic Reciprocity - Numericana
		Quadratic residues: Half of the nonzero residues modulo an odd prime p.
		Euler's criterion: A quadratic residue raised to the power of (p-1)/2 is 1.
		In particular, g itself can't be a quadratic residue (the order of g must be p-1, and it would be at most (p-1)/2 if g was congruent to the square of some x, since the order of x divides p-1, by Fermat's little theorem).
	home.att.net /~numericana/answer/reciprocity.htm (1523 words)

	Quadratic equation Summary
		A quadratic equation is an equation of the second degree, meaning that for an equation in x, the greatest exponent on x is 2.
		The theory involving quadratic equations, and all polynomial equations, was flawed prior to the 17th century because of this idea.
		In mathematics, a quadratic equation is a polynomial equation of the second degree.
	www.bookrags.com /Quadratic_equation (3488 words)

	GRAPHS OF QUADRATIC EQUATIONS (Site not responding. Last check: )
		Every quadratic equation has at most two solutions, but for some equations, the two solutions are the same number, and for others, there is no solution on the number line (because it would involve the square root of a negative number, which makes it imaginary).
		When you set the quadratic equation equal to zero, this represents the points where the parabola hits the x-axis (the x-intercepts, where y=0).
		Where the parabola hits on the x-axis is the solution(s) to the quadratic equation.
	www.tcnj.edu /~martin28/graphs_of_quadratic_equations.htm (122 words)

	Quadratic Equations
		A quadratic equation thus requires that a single variable be present, and that the variable be raised to the second, first, and zero power.
		Quadratic equations always have two roots, which can either be real or imaginary.
		For example, if we are using the quadratic equation to solve for the concentration of a reactant, a negative value would be meaningless.
	web.uccs.edu /slc/modules/chem106/quadratic_equations.htm (774 words)

	Quadratic Functions
		Solving a quadratic equation means finding the places where the parabola crosses the x-axis on a coordinate grid.
		The vertex form of a quadratic function is probably the most useful when graphing a parabola because you can read off the location of the vertex of the parabola directly from the equation.
		It is the form you get when you solve a quadratic equation using the completing the squares method.
	www.capitan.k12.nm.us /teachers/shearerk/quadratic_functions.htm (371 words)

	Quadratic Functions
		Note that when a quadratic function is in standard form it is also easy to find its zeros by the square root principle.
		If the graph of a quadratic function has two x-intercepts, then the line of symmetry is the vertical line through the midpoint of the x-intercepts.
		A is a quadratic function of x, and the graph opens downward, so the highest point on the graph of A is the vertex.
	www.uncwil.edu /courses/mat111hb/Pandr/quadratic/quadratic.html (1269 words)

	Developing for Developers : Factoring large numbers with quadratic sieve
		Half of all numbers are quadratic residues mod p, regardless of the value of p, and there's a simple formula for determining whether or not a particular number is: just take a, raise it to the power (p−1)/2, and then take the remainder after division by p.
		Quadratic sieve admits a number of "bells and whistles" to dramatically improve its runtime in practice.
		It's rare to find an implementation of quadratic sieve in a high-level language because it depends on an efficient implementation of arbitrary-precision integers and reduction of sparse 0/1 matrices, which are easier to pull off in C, C++, or assembly language.
	blogs.msdn.com /devdev/archive/2006/06/19/637332.aspx (3836 words)

	BioMath: Quadratic Functions
		You can solve quadratic equations by completing the square, using the quadratic formula, or, in rare cases, by factoring.
		In most cases, solving quadratic equations is most easily accomplished using the quadratic formula.
		In some cases, using the quadratic formula is not necessary to solve a quadratic equation.
	www.biology.arizona.edu /biomath/tutorials/Quadratic/SolvingQuadraticEquations.html (468 words)

	BioMath: Quadratic Functions
		A quadratic function is graphically represented by a parabola with vertex located at the origin, below the x-axis, or above the x-axis.
		Since the quadratic formula requires taking the square root of the discriminant, a negative discriminant creates a problem because the square root of a negative number is not defined over the real line.
		If the discriminant of a quadratic function is equal to zero, that function has exactly one real root and crosses the x-axis at a single point.
	www.biology.arizona.edu /BioMath/tutorials/Quadratic/Roots.html (613 words)

	Algebra II: Quadratic Equations - Text-only
		Quadratic equations, or equations of the second degree, such as x^2 + 2x - 5 are probably the most common equation you will see in Algebra II (intermediate algebra).
		Quadratic equations of type ax^2 + bx + c = 0 and ax^2 + bx = 0 (c is 0) can be factored to solve for x.
		Quadratic equations of type ax^2 + c = 0 can be solved by solving for x.
	library.advanced.org /20991/textonly/alg2/quad.html (591 words)

	[No title]
		There are two roots (answers) to a quadratic equation, because of the in the equation.
		Midrash is like a quadratic equation or a very complex second order differential equation, a thirteen or fourteen step equation.
		The quadratic regression option finds the equation of a quadratic equation of the form y = ax2 + bx + c that best fits a set of data.
	www.lycos.com /info/quadratic-equation.html?page=2 (345 words)

	Solving Quadratic Equations (Site not responding. Last check: )
		Any equation, whether it be linear, quadratic, exponential or some other type of equation, is asking you to solve for the variable in the equation.
		If an equation is not in standard form, we must manipulate it until it is. If you link to the lessons on solving by factoring or solving by using the quadratic formula, you will see that we must always begin with the standard form.
		There are a lot of terms used simultaneously and interchangeably when working with quadratics and many students get confused about what they are trying to do.
	www.algebralab.org /lessons/lesson.aspx?file=Algebra_quad_solve.xml (297 words)

	The Prime Glossary: quadratic residue
		In the study of diophantine equations (and surprisingly often in the study of primes) it is important to know whether the integer a is the square of an integer modulo p.
		If it is, we say a is a quadratic residue modulo p; otherwise, it is a quadratic non-residue modulo p.
		One of the most important results about quadratic residues is expressed in the surprisingly difficult to prove quadratic reciprocity theorem (see the entry on the Legendre symbol).
	primes.utm.edu /glossary/page.php?sort=QuadraticResidue (168 words)

	The Quadratic Function
		In this case the quadratic formula is given by
		Notice that the graph of the quadratic function is a parabola.
		Solve the equation by means of the quadratic formula where a = 231, b = -20, and c = -4.
	www.columbia.edu /itc/sipa/math/quadratic.html (335 words)

	Quadratic Residue (Site not responding. Last check: )
		The deepest of the results regarding quadratic residues was first proven rigorously by Gauss, and is known as the Quadratic Reciprocity Law.
		Mathworld's article, Quadratic Residue includes a table giving the primes which have a given number, d, as a quadratic residue (left).
		Mathpages: The Jewel of Arithmetic: Quadratic Reciprocity -- Euler's Criterion for quadratic residue is that
	mcraefamily.com /MathHelp/BasicNumberSquareQuadraticResidues.htm (1244 words)

	Quadratic Equations
		Quadratic equations are used in many areas of science and engineering.
		The quadratic equation is often used in modelling because it is a beautifully simple curve.
		The parabola is closely related to the quadratic equation
	www.intmath.com /Quadratic-equations/Quadratic-equations-intro.php (202 words)

	TI-83/84 Plus BASIC Quadratic Solvers - ticalc.org
		Math Program in which user inputs coefficients of a quadratic equation and finds out what X equals and how the equation is factored.
		Quadratic equation solver with real/imaginary roots in decimal/fraction form, interactive graphing,table of values, descriminant, vertex, and Y-int.
		QUAD is a program that is a quadratic equation solver, both real and imaginary roots are displayed.
	www.ticalc.org /pub/83plus/basic/math/quadratic (3005 words)

	TI-83/84 Plus BASIC Quadratic Solvers - ticalc.org
		My program doesn't have the extra needless features that other quadratic programs have; there are no nagging screens at the beginning telling you who wrote it.
		I know the last thing this archive needs is another quadratic formula program but this one is different from the other ones.
		A quadratic formula program that gives you X values in fractions when possible and vertex values for the parabola.
	www.ticalc.org /pub/83plus/basic/math/quadratic/date.html (3005 words)

	The Quadratic Formula Explained
		But sometimes the quadratic is too messy, or it doesn't factor at all, or you just don't feel like factoring.
		So, while factoring may not always be successful, the Quadratic Formula can always find the solution.
		This can be useful if you have a graphing calculator, because you can use the Quadratic Formula (when necessary) to solve a quadratic, and then use your graphing calculator to make sure that the displayed
	www.purplemath.com /modules/quadform.htm (0 words)

	College Algebra Tutorial on Graphs of Quadratic Functions
		The graph of a quadratic function is called a parabola and has a curved shape.
		Note that in a quadratic function there is a power of two on your independent variable and that is the highest power.
		Use the vertex and the intercepts to sketch the graph of the given quadratic function.
	www.wtamu.edu /academic/anns/mps/math/mathlab/col_algebra/col_alg_tut34_quadfun.htm (1601 words)

	Quadratic formula
		Roots of quadratics always come in pairs, but when there are two roots that are the same we say that there is only one root.
		The quadratic formula is derived from the general quadratic equation (below) by completing the square.
		These values are found from the quadratic equation as described in the ‘theory’ section at the top of this article, and you need to identify ‘a’, ‘b’, and ‘c’ and write their values down.
	www.teacherschoice.com.au /Maths_Library/Algebra/Alg_6.htm (783 words)

Try your search on: Qwika (all wikis)