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	Quadratic equation - Wikipedia, the free encyclopedia
		In mathematics, a quadratic equation is a polynomial equation of the second degree.
		This equation may be resolved directly or with a simple substitution, using the methods that are available for the quadratic, such as factoring (also called factorising), the quadratic formula, or completing the square.
		Shridhara was said to be one of the first mathematicians to give a general rule for solving a quadratic equation.
	en.wikipedia.org /wiki/Quadratic_formula (900 words)

	Quadratic equation -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		The quadratic formula explicitly gives the solutions of a quadratic equation in terms of the coefficients a, b and c, which we temporarily assume to be (An old small silver Spanish coin) real (but see below for generalizations) with a being non-zero.
		Geometrically, this means that the (A plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the curve) parabola described by the quadratic equation touches the x-axis in a single point.
		The quadratic formula is derived by the method of (Click link for more info and facts about completing the square) completing the square.
	www.absoluteastronomy.com /encyclopedia/q/qu/quadratic_equation.htm (966 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)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-11-07)
		There are quite a few methods to solve a quadratic equation, and you have asked about the quadratic formula, so I'll concentrate on this for you.
		The part of the formula (b^2 - 4ac) that is under the square root sign is called the discriminant.
		When you come to using the quadratic equation for modeling, it will probably be the case that one of these answers is not appropriate.
	mathforum.org /library/drmath/view/53198.html (1180 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-11-07)
		The quadratic formula, -b +/- sqrt(b^2 - 4ac) x = ----------------------- 2a applies whenever you have an equation like ax^2 + bx + c = 0 So we can start with either the formula, or the equation.
		The standard quadratic form ax^2 + bx + c = 0 is exactly equivalent to the quadratic formula -b +/- sqrt(b^2 - 4ac) x = ---------------------- 2a So you could 'undo' the formula, and then proceed as I proceeded.
		By noticing that the standard quadratic equation and the quadratic formula are equivalent, I saw that I could reduce either one to the other, which meant that I could choose either as my starting point, knowing that a conversion between the two existed.
	mathforum.org /library/drmath/view/52370.html (876 words)

	83 Plus Quadratic Formula
		Prova, Utah) An Inertia Formula for Hermitian Matrices With...
		L is given by the formula A = LW.
		therefore the likelihood function is not quadratic and the standard methods for its analysis are...
	quadraticformula.sawsformula.com /83plusquadraticformula (774 words)

	Quadratic Formula (Site not responding. Last check: 2007-11-07)
		The quadratic is probably the second most famous formula in mathematics.
		The most basic is the square root property, which tells us that when a variable squared is equal to a positive constant, the variable can be either the principal square root or the negative square root of the constant.
		1.) The equation is a quadratic with dominant coefficient one.
	www.geocities.com /profzeta/QuadraticFormula/Quadratic.htm (324 words)

	Math Help - Algebra - Quadratics - Theory - Graphs
		There are three important cases of quadratics depending on where the graph crosses the x-axis (these points are called roots or zeros of the equation).
		In general, there are two big things we want to do with a quadratic equation: solve it for all possible values of x, or graph the equation.
		There are three main methods of solving quadratics: Guessing the solutions (also known as the double parentheses method), completing the square, and using the quadratic formula.
	www.hyper-ad.com /tutoring/math/algebra/Quadratic_theory.html (1403 words)

	101 uses of a quadratic equation: Part II
		In this quadratic expression we see stark evidence as to why we should slow down in urban areas, as a small reduction in speed leads to a much larger reduction in stopping distance.
		The simple quadratic formula relating time to distance is also the basis of the science of ballistics, which looks at the way that objects move under gravity.
		However, this quadratic equation is accurate enough to predict the behaviour of the flow of air over the wing of an aircraft and to see why an aircraft flies.
	plus.maths.org /issue30/features/quadratic/index-gifd.html (4300 words)

	SparkNotes: New SAT: Binomials and Quadratic Equations
		Quadratics are the robots who return from the future to destroy humankind at the end of Terminator 3.
		On the SAT, you’ll be able to factor almost every quadratic expression or equation that appears, but every once in a while the test may throw in a quadratic that you need to know the quadratic formula to solve.
		The roots of the quadratic are approximately {–4.303, –0.697}.
	www.sparknotes.com /testprep/books/newsat/chapter19section8.rhtml (1281 words)

	The Quadratic Formula and Solutions to Quadratic Equations (Site not responding. Last check: 2007-11-07)
		Solving a quadratic equation using the zero factor property only works when, after the equation is set equal to zero, the resulting polynomial is factorable.
		Solving a quadratic equation by completing the square always works, but can easily become quite tedious.
		If a general quadratic equation in standard form is solved for x by completing the square, the result is an easy to use formula called the quadratic formula.
	cwx.prenhall.com /bookbind/pubbooks/tobey3/medialib/course_notes/ch08_quadratic_equations/quad_formula.htm (400 words)

	Quadratic Equations and Inequalities - The Quadratic Formula (Site not responding. Last check: 2007-11-07)
		Quadratic Equations and Inequalities - The Quadratic Formula
		The quadratic formula is used to solve unfactorable quadratic equations.
		It provides a way to find roots for the quadratic formula without solving the whole equation.
	library.thinkquest.org /10030/5quadfor.htm (175 words)

	PlanetMath: derivation of quadratic formula (Site not responding. Last check: 2007-11-07)
		"derivation of quadratic formula" is owned by mathcam.
		Cross-references: derivation, formula, solution, sides, square root, identity, completing the square, equation, divide, real numbers
		This is version 7 of derivation of quadratic formula, born on 2001-11-07, modified 2004-09-12.
	planetmath.org /encyclopedia/DerivationOfQuadraticFormula.html (109 words)

	Algebra (Math 1314) - Solving Equations and Inequalities - Quadratic Equations - Part II (Site not responding. Last check: 2007-11-07)
		The topic of solving quadratic equation has been broken into two sections for the benefit of those viewing this on the web. As a single section the load time for the page would have been quite long. This is the second section on solving quadratic equations.
		Both of the solution methods we looked at in the previous section will not always work. Not every quadratic is factorable and not every quadratic is in the form required for the square root property. It is now time to start looking into methods that will work for all quadratic equations.
		The important part here is to make sure that before we start using the quadratic formula that we have the equation in standard form first.
	tutorial.math.lamar.edu /AllBrowsers/1314/SolveQuadraticEqnsII.asp (1754 words)

	The Quadratic Formula (Site not responding. Last check: 2007-11-07)
		The solutions to a quadratic equation can be found directly from the quadratic formula.
		As a general rule you should look at a quadratic and see if it can be solved by taking square roots; if not, then if it can be easily factored; and finally use the quadratic formula if there is no easier way.
		The quadratic formula can be derived by using the technique of completing the square on the general quadratic formula:
	www.jamesbrennan.org /algebra/quadratics/the_quadratic_formula.htm (263 words)

	Quadratic Formula and roots of a cubic
		Author: yendor It is well known that there is a quadratic formula which finds the two roots of ax^2 + bx + c = 0 (a does not equal 0).
		Furthermore, the formula itself is kind of cumbersome: if the cubic has three real roots, the formula requires the user to calculate cube roots of complex numbers, even though the imaginary parts end up canceling each other out.
		The formula is used by all of the symbolic algebra packages (Mathematica, Macsyma, etc.) that I have seen, probably simply because it is general (works for all cubics, even those with complex coefficients).
	www.newton.dep.anl.gov /newton/askasci/1995/math/MATH052.HTM (611 words)

	A Hotlist on Quadratic Formula (Site not responding. Last check: 2007-11-07)
		Quadratic Equations - This site explains multiple ways to solve a quadratic equation, and explains what the solutions mean.
		Quadratic Equation Solver - This site allows you to enter values for a,b,c; and gives you the solution.
		Derivation of the Quadratic Formula - This site takes you through the steps involved in deriving the quadratic formula.
	www.kn.pacbell.com /wired/fil/pages/listquadratimr1.html (112 words)

	Algebra (Math 1314) - Solving Equations and Inequalities - Quadratic Equations : A Summary (Site not responding. Last check: 2007-11-07)
		So, in the previous two sections we’ve talked quite a bit about solving quadratic equations. A logical question to ask at this point is which method should we use to solve a given quadratic equation? Unfortunately, the answer is, it depends.
		These are the ONLY possibilities for solving quadratic equations in standard form. Note however, that if we start with rational expression in the equation we may get different solution sets because we may need avoid one of the possible solution so we don’t get division by zero errors.
		Now, it turns out that all we need to do is look at the quadratic equation (in standard form of course) to determine which of the three cases that we’ll get. To see how this works let’s start off by recalling the quadratic formula.
	tutorial.math.lamar.edu /AllBrowsers/1314/SolveQuadraticEqnSummary.asp (764 words)

	Quadratic Equations (Site not responding. Last check: 2007-11-07)
		Objective: Students will be able to solve quadratic equations with perfect squares.
		Quadratic equation with a perfect square has the form of (ax+b)
		Quadratic equation with a perfect square can be solved in three steps.
	www.gomath.com /htdocs/lesson/quadratic_lesson1.htm (129 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)

	Quadratic Formula (C)
		A quadratic equation is an equation of the form
		If either B or C is zero, it is more efficient to solve quadratic equations by factoring.
		Derive the quadratic formula by completing the square.
	www.uwm.edu /People/ericskey/TANOTES/Algebra/node10.html (210 words)

	Revision Centre - GCSE Maths - Algebra - Quadratic Equations (Site not responding. Last check: 2007-11-07)
		A quadratic equation is an equation where the highest power of x is x².
		Some people don't like the method of completing the square to solve equations and an alternative is to use the quadratic formula.
		Sometimes, quadratic equations can be solved by factorising.
	www.revisioncentre.co.uk /gcse/maths/quadratic_equations.html (537 words)

	Quadratic etc equations
		In about 300 BC Euclid developed a geometrical approach which, although later mathematicians used it to solve quadratic equations, amounted to finding a length which in our notation was the root of a quadratic equation.
		Al-Khwarizmi gives the rule for solving each type of equation, essentially the familiar quadratic formula given for a numerical example in each case, and then a proof for each example which is a geometrical completing the square.
		The irreducible case of the cubic, namely the case where Cardan's formula leads to the square root of negative numbers, was studied in detail by Rafael Bombelli in 1572 in his work Algebra.
	www-gap.dcs.st-and.ac.uk /~history/HistTopics/Quadratic_etc_equations.html (1457 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Solving a quadratic equation means finding the values of x where the graph cuts the x-axis.
		The graph for a quadratic equation is a parabola.
		If the parabola cuts the x-axis at only one point it means that the quadratic equation has two solutions with the same value (the value of x where the parabola touches the x-axis).
	www.cne.gmu.edu /modules/dau/algebra/equations/quad2_bdy.html (347 words)

	Factoring: The Quadratic Formula (Site not responding. Last check: 2007-11-07)
		You may be interested to know the quadratic formula can be derived fairly easily using the concepts of the perfect square trinomial and the difference of two squares.
		Before I show you a method of deriving the quadratic formula, would you like to see a page about finding two numbers if you know their sum and their product?
		The graph has the shape of a parabola, which is the trajectory a ball follows when it is thrown.
	www.mcraeclan.com /MathHelp/factoring4.htm (918 words)

	The Quadratic Formula (Site not responding. Last check: 2007-11-07)
		In the last two documents on the quadratic equations we have looked at equations that are perfect square trinomials, in which case we are able to factor the equation into two prime binomials.
		Once the equation is factored, we use the zero factor property to arrive at values of the variable for which the equation is satisfied.
		In the event that we cannot factor or complete the square, a quadratic equation may be solved by use of the quadratic formula:
	home.earthlink.net /~ubingc/math/mth209/soln3.htm (588 words)

	The Quadratic Formula
		is the expression inside of the square root sign in the quadratic formula.
		is a positive number, then the quadratic formula will produce two roots (one for the plus and one for the minus).
		If we know the roots of a quadratic then it is easy to find the original quadratic by using the zero product formula in reverse.
	www.ltcconline.net /greenl/courses/152B/QuadraticsLineIneq/quadfor.htm (239 words)

	Quadratic Formula (Site not responding. Last check: 2007-11-07)
		Below is a variation of the quadratic formula.
		Arithmetic precision and weather or not rescaling has occured affects the computational error of the quadratic formula.
		Compare the results of this bottom window with the results calculated in the current precision using both variations of the quadratic formula found on the right.
	www.mste.uiuc.edu /exner/ncsa/quad (246 words)

	Quadratic Formula (Site not responding. Last check: 2007-11-07)
		You can solve this equation by directly substituting the values of a, b, and c into the quadratic formula.
		we have many quadratic formulas for which we cannot easily see what the factors are.
		Apply the quadratic formula where a= 5, b = 10, and c=3.
	www.unf.edu /~tbratina/mathed/lesson/quadraticformula.htm (263 words)

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