Math Hl Type 1 Shadows - 3091 Words

Higher Level Mathematics Internal Assessment Type I Shadow Functions Contents Introduction: Functions/Polynomials 3 Part A: Quadratic Polynomials 4 Part B: Cubic Polynomials 12 Introduction: In mathematics, function is defined as a relationship, or more of a correspondence between the set of input values and the set of output values. Also, a rule is involved, or as it may be referred to, a ‘set of ordered pairs’ that assigns a unique output for each of the input. The output correspondence is usually defined as f and the output is x. The correspondence is denoted as f(x). All functions are mainly defined by two factors, as was mentioned before, set of inputs - which are called arguments; and outputs - which†¦show more content†¦So it can be said that: -(x+2)2-9+18 = -Y1+2Ym = Y2 At this point, the real and imaginary components of the complex zeros of Y1 can be found using the values for zeros of Y2. As it is known, Y1 has complex zeros of a form of a ±ib and Y2 has zeros of a ±b. With this information available, I will show you how to obtain value for complex zeros of Y1. Consider a function Y1, with a general statement of: Y1 = (x-a)2+b2 As it has been found earlier, this function has zeros of a ±ib. It also has a shadow function Y2: Y2 = -(x-a)2+b2 With zeros of a ±b. If we say that a = 2 and b = -3, then this function has zeros of 2 ±(-3). In this form of zeros, we can say that 2 is the x value of the vertex coordinates, lying on the axis of symmetry of Y2 on the x-axis, and  ±3 are just the distances between the mid point 2 to the points where Y2 intersects x-axis. It is clearly shown on the graph below. As we know the zeros of Y2, it will be very easy to determine the complex zeros of Y1. 2 will equal to the real part of the complex zeros of Y1, and subsequently,  ±3 will equal to the imaginary part of the complex roots. Although, as we know that y-axis is the imaginary axis, the imaginary parts of the complex roots obtained, of the Y1, will be plot according to the y-axis. As you may have observed, in order to get the complex zeros ofShow MoreRelatedProject Managment Case Studies214937 Words   |  860 Pagesmanagement : case studies I Harold Kerzner. -- 2nd ed. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-471-75167-0 (pbk.) ISBN-10: 0-471-75167-7 (pbk.) 1. Project management-Case studies. I. Title. Printed in the United States of America Contents Preface xi 1 PROJECT MANAGEMENT METHODOLOGIES 1 Lakes Automotive 3 Fems Healthcare, Inc. Clark Faucet Company 2 5 7 11 IMPLEMENTATION OF PROJECT MANAGEMENT Kombs Engineering 13 Williams Machine Tool CompanyRead MoreOne Significant Change That Has Occurred in the World Between 1900 and 2005. Explain the Impact This Change Has Made on Our Lives and Why It Is an Important Change.163893 Words   |  656 Pagestwentieth century history / edited by Michael Peter Adas for the American Historical Association. p. cm.—(Critical perspectives on the past) Includes bibliographical references. ISBN 978-1-4399-0269-1 (cloth : alk. paper)—ISBN 978-1-4399-0270-7 (paper : alk. paper)—ISBN 978-1-4399-0271-4 (electronic) 1. History, Modern—20th century. 2. Twentieth century. 3. Social history—20th century. 4. World politics—20th century. I. Adas, Michael, 1943– II. American Historical Association. D421.E77 2010