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Topic: Quartic function

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Quartic equation

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	Encyclopedia: Function (mathematics)
		A very common type of function occurs when the argument (input) and the value (output) are both numbers, the functional relationship is expressed by a formula, and the value (output) of the function is obtained by direct substitution of the argument into the formula.
		Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions.
		The number of computable functions from integers to integers is countable, because the number of possible algorithms is. The number of all functions from integers to integers is higher: the same as the cardinality of the real numbers.
	www.nationmaster.com /encyclopedia/Function-(mathematics) (6715 words)

	Quartic equation - Wikipedia, the free encyclopedia
		In mathematics, a quartic equation is the result of setting a quartic function equal to zero.
		As with other polynomials, it is sometimes possible to factor a quartic equation directly; but more often such a feat is Herculean, especially when the roots are irrational or complex.
		After much effort, such a formula was indeed found for quartics — but since then it has been proven (by Evariste Galois) that such an approach dead-ends with quartics; they are the highest-degree polynomial equations whose roots can be expressed in a formula using a finite number of arithmetic operators and n-th roots.
	en.wikipedia.org /wiki/Quartic_equation (1529 words)

	CURVE (Lat. curvus, bent) - Online Information article about CURVE (Lat. curvus, bent)
		A quartic curve has 28 double tangents, their points of contact determined as the intersections of the curve by a curve II= o of the order 14, the equation of which in a very elegant form was first obtained by Hesse (1849).
		The theory of the invariants and covariants of a ternary cubic function u has been studied in detail, and brought into connexion with the cubic curve u=o; but the theory of the invariants and covariants for the next succeeding case, the ternary quartic function, is still very incomplete.
		Or again, we may have a quartic curve having a cusp at each of the circular points: such a curve is a " Cartesian," it being a complete definition of the Cartesian to say that it is a bicuspidal quartic curve (m=4, 3=o, K= 2), having a cusp at each of the circular points.
	encyclopedia.jrank.org /CRE_DAH/CURVE_Lat_curvus_bent_.html (8727 words)

	assignment7
		In order to discuss functions I feel it is important to discuss the difference between relations and functions and also define what an inverse is as it relates to a function.
		In the case of this function, y = 5 is a horizontal asymptote and in the case of the inverse relation of this funciton, x = 5 is a vertical asymptote.
		We have looked a several different types of functions encountered in high school mathematics classes of which some produced inverse relations that were functions and others produced inverse relations that were not functions.
	web.pdx.edu /~jdtalley/Homework/assignment7/invsfunctions.html (1681 words)

	Graphing Polynomial Functions - Cubic and Quartic E quations
		, a polynomial, a quartic equation, of degree 4.
		That is to say, the third degree polynomial had three roots, and the fourth degree polynomials had four roots, some were at an inflection point and some were a double root.
		The 3d degree polynomials, F1 and F2, were similar in that as x became smaller and smaller, the function steadily decreased or (became more negative), and as x increased beyond the rightmost root, the function steadily increased.
	www.theoldpro.net /math/graphingpolynomials (978 words)

	[No title]
		When less than 1, // the ellipsoids are oblate, // when greater than 1 the ellipsoids are prolate, // when zero the ellipsoids are spherical // (and hence the whole surface is a sphere) // 2.
		When less than 1, the ellipsoids are oblate, // when greater than 1 the ellipsoids are prolate, // when zero the ellipsoids are spherical // (and hence the whole surface is a sphere) // 2.
		Controls the width of the tube and the vertical scale of the "egg" #declare f_r = function { internal(57) } // Parameters: x, y, z // no extra parameters required #declare f_ridge = function { internal(58) } // Parameters: x, y, z // Six extra parameters required: // 1.lambda // 2.
	www.tyskaskolan.se /povray/functions.inc (3075 words)

	unit03-sect03-les03-lessone (Site not responding. Last check: 2007-10-22)
		To write the equation or function notation for a particular quartic function using this method, we need its real zeros and some way of determining the value of a.
		The function notation for the graph is thus: f(x) = -
		We seen in the previous lessons that it is possible for a quartic to have two or four complex roots and hence its graph will only have two x-intercepts or not have any x-intercepts at all.
	www.cdli.ca /courses/math3103/unit03/section03/lesson03/3-lesson-e.htm (549 words)

	Quartic function - Wikipedia, the free encyclopedia
		A quartic function is a function of the form
		with nonzero a; or in other words, a polynomial function with a degree of four.
		Such a function is sometimes called a biquadratic function, but the latter term can occasionally also refer to a quadratic function of a square, having the form
	en.wikipedia.org /wiki/Quartic_function (158 words)

	Isosurface Tutorial: i_algbr Library part 3
		The Quartic paraboloid is similar to a paraboloid, but has a squarer shape.
		The Quartic saddle is similar to a saddle, but has a squarer shape.
		To produce a surface that matches the 3d version, the height parameter needs to be the square of the size parameter.
	www.econym.demon.co.uk /isotut/builtin4.htm (523 words)

	Quartic - Wikipedia, the free encyclopedia
		In mathematics and elsewhere, the adjective quartic means fourth order, such as the function x
		A quartic number is a number which equals the fourth power of an integer.
		This page was last modified 01:57, 11 June 2005.
	en.wikipedia.org /wiki/Quartic (55 words)

	3.1 - Quadratic Functions
		A function with one variable raised to whole number powers (the largest being n) and with real coefficients.
		A polynomial function in one variable of degree 0.
		A polynomial function in one variable of degree 1.
	www.richland.edu /james/lecture/m116/polynomials/quadratics.html (633 words)

	Quintic function - TheBestLinks.com - Derivative, Polynomial, Function (mathematics), Cubic function, ... (Site not responding. Last check: 2007-10-22)
		Quintic functions are polynomial functions in which the highest degree is five.
		Because they have an odd degree, normal quintic functions appear similar to normal cubic functions when graphed, except for the fact that they may possess an additional local maximum and minimum each.
		The derivative of a quintic function is a quartic function.
	www.thebestlinks.com /Quintic.html (113 words)

	Chapter 2 Study Tips
		Emphasizing a linear function as a function with a constant rate of change is an important "pre-calculus" feature of this section.
		The underlying algebra (e.g., linear functions, vertex of a parabola) might be familiar to you, but the context in which it is presented will be new to most students.
		Although half of the "ten basic functions" of Section 1.3 are actually power functions, it took the addition of "power regression" on calculators to earn them the status of their own section in the textbook.
	occawlonline.pearsoned.com /bookbind/pubbooks/demana_awl/chapter1/medialib/studytips/chapter2.html (2140 words)

	[No title]
		True or false: if f is a polynomial function, then so are the fest and second derivatives; therefore we don’t need to worry about where f, f’, and f” do not exist.
		f is a quartic polynomial function with two double roots and a y intercept of 5 b.
		A rectangular ostrich pen that is divided into six equal sections by two interior fences that run parallel to the east and west fences, and another interior fence running parallel to the north and south fences.
	www.math.jmu.edu /~taal/231_2003fpost/jamie3.doc (516 words)

	GONG IRAF help pages (Site not responding. Last check: 2007-10-22)
		Function is: PRM1 * COS(PRM2X + PRM3Y + PRM4) X and Y are relative to X0, Y0.
		QUART This option calculates a quartic function of X,Y (rotated according to the rotation matrix ROT) in pixel array DAT(NX,NY).
		Function is: PRM1 * ((X - PRM2)2 + (Y - PRM3)2)**2 X and Y are relative to X0, Y0.
	gong.nso.edu /data/iraf_help/expand.html (366 words)

	BBC Education - AS Guru - Maths - Methods - Differentiation - Stationary Points
		Polynomial functions will produce graphs of varied shape, but common to most of them will be features as in the figure (this is a quartic function, i.e.
		Stationary points on this curve are A, B and C. Immediately to the left of both A and C, the value of the function is increasing and its derivative is positive.
		At A and C, the function is neither increasing nor decreasing, hence the description "stationary".
	www.bbc.co.uk /education/asguru/maths/12methods/03differentiation/17stationary/index.shtml (472 words)

	Function of a Function
		is a cubic function of a quadratic function
		is a square root function of a quartic function
		One of the most important properties of an exponential function is that the slope of the function at any value is proportional to the value of the function itself.
	www.chm.bris.ac.uk /~paulmay/misc/1s/calclt6.htm (321 words)

	A Function of Time, Frequency, Lag, and Doppler - O'Neill, Williams (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		They are the signal in time, the spectrum, the auto-correlation function of the signal, and the auto-correlation function of the spectrum.
		The variables of these functions are denoted, respectively, as time, frequency, lag, and doppler.
		In time-frequency analysis, these functions of one variable are extended to quadratic functions of two variables.
	citeseer.ist.psu.edu /97696.html (467 words)

	Precalculus: Graphs and Models, A Unit Circle Approach Chapter 3 -- Data Set Exercises
		Using the function from part b that best fits, predict the weight of an alligator that is 95 inches long.
		Use a grapher to determine whether a cubic or quartic function best fits this data by comparing the value of R2.
		Use this function to estimate what the price was in week 26.
	occawlonline.pearsoned.com /bookbind/pubbooks/bittinger8_awl/chapter3/custom4/deluxe-content.html (245 words)

	DSmanual (Site not responding. Last check: 2007-10-22)
		There are three ways of doing this: wrap your function directly in a file called objective.cc; send the function name in as a parameter to a constructor (but some rewriting will almost certainly have to be done there as well); or use our
		The function fcn_eval() (in our objective.cc file) calls EvalF(), uses the UNIX fork and exec calls to spawn a child process and superimpose the user's objective function upon the child process.
		We realize that there will be times when the standard deviation test will actually take more function calls than the ``delta'' test, but this is not typically the case, and we make this compromise for the sake of efficiency.
	www.cs.wm.edu /~plshep/manual (3070 words)

	Math Online Q and A: graph a polynomial f(x)=-1/3(x+2)(x+4)^2(3x-1)I a (Site not responding. Last check: 2007-10-22)
		This is a 4th degree polynomial also called a quartic function.
		We are trying to determine of the functions graph would be above the x-axis for x-values between the roots or would it be below (negative) This will help us see the graph's movement on the coordinate plane.
		We know this because in order for the function to ever be positive again, the grpah would have to pss through the x-axis again forming another root.
	www.mathonline.org /mho/view.cgi?21144 (655 words)

	CMATH: Complex Number Math Functions for PC Compilers
		All functions may alternatively be called from classic C and Pascal/Delphi with type-specific function names (like cf_sin, cd_exp, pe_sqrt), or from C++ and Delphi with overloaded function names and operators (like sin, exp, sqrt, operator +; operators only in C++).
		The single exception is the member function polar, which had to be replaced by magargtoc, as the word "polar" now denotes the complex classes in polar coordinates.
		Note, however, that the member function polar had to be replaced by magargtoc, as the name "polar" is now reserved for the polar classes.
	www.optivec.com /cmfuncs (2912 words)

	PreCalculus
		A local minimum or local maximum of a function is an extreme value.
		A local extreme value may exist within an arbitrary open interval in the domain of a function.
		These extreme values occur only at critical points where the slope of a line tangent to the graph is zero.
	home.att.net /~srschmitt/precalc/precalc-11-03-01.html (279 words)

	Introduction to Graphing of Polynomial Functions-Chapter 6 Section 7 (Site not responding. Last check: 2007-10-22)
		Some polynomials functions are given special names according to their degrees.
		+20 is called a quartic function; its degee (power on the x variable) is four.
		The graph of every quadratic function is a parabola and has an axis of symmetry; the vertical line tht passes through the vertex of the parabola.
	www.rose.edu /faculty/gjackson/elealg/each6-7.htm (839 words)

	A Linear Mini-Max Estimator for the Case of a Quartic Loss Function - Helmes, Srinivasan (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		We consider the problem of estimating the value L(`), where L is a known continuous linear function defined on \Theta, using linear estimators of the form hm; yi = R m(t)dY (t); m 2 L 2 [0; 1].
		We solve the problem for the case of a quartic loss function, and compare the...
		Helmes, K. and Srinivasan, C. A linear mini-max estimator for the case of a quartic loss function, to appear in Random Oper.
	citeseer.ist.psu.edu /helmes00linear.html (488 words)

	ipedia.com: Quartic equation Article (Site not responding. Last check: 2007-10-22)
		An example of a quartic equation is the equation the general form is As the fundamental theorem of algebra...
		The depressed quartic can be solved by means of a method discovered by Ferrari.
		(see sign function) will be indeterminate, but in such a case equation (1) becomes equivalent to a quadratic equation so that it is possible to use the quadratic formula to solve for u
	www.ipedia.com /quartic_equation.html (1078 words)

	1_30notes (Site not responding. Last check: 2007-10-22)
		A linear function f(x) = ax + b is a polynomial function of degree one.
		Graphs of Polynomial Functions are smooth continuous curves that have no holes, no breaks, and no sharp corners.
		The domain of a rational function f(x) = g(x)/h(x) is the set of all real numbers such that h(x) is not zero.
	www-math.cudenver.edu /~llana/1_30notes.html (365 words)

	Java Applets (Site not responding. Last check: 2007-10-22)
		Apply the slope formula to the points reported by the applet and verify that the slope is -0.75.
		The applet below illustrates the fact that five points in the plane determine a degree four polynomial (quartic) function.
		The quartic function determined by the points is written in the text box below the graph, and its graph is drawn in the coordiante plane.
	www.uncwil.edu /courses/mat111hb/demo/applets.html (211 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		S(t) quartic spline interpolation function EMBED Equation.3 quartic B-spline function ci coefficients of spline function f(x) original function Introduction Splines are used to interpolate data with m-splines being the most commonly used.
		Our data is taken from the sin x function, where the number of samples are 15, starting from 0 to 30 evenly spaced (see Table 2 for the array and corresponding y values).
		Results By means of quartic spline interpolation routine developed in this work, we interpolated the experimental data above and plotted the original function and its interpolated graph (see Figure 1).
	www.msu.edu /~gumussoy/cv/project3.doc (1542 words)

	Quartic function -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		Quartic function -- Facts, Info, and Encyclopedia article
		The ((linguistics) a word that is derived from another word) derivative of a quartic function is a (additional info and facts about cubic function) cubic function.
		Finding Roots: See (additional info and facts about Quartic equation) Quartic equation.
	www.absoluteastronomy.com /encyclopedia/q/qu/quartic_function.htm (107 words)

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