learned how to determine the zeros of a function through various algebraical methods and graphically and solving quadratic equations in the complex number system. With these skills and concepts, I was able to apply them to real-world situations. This portfolio shows the various methods to determine the zeros of a quadratic functions. I had learned the four different methods: solve by factoring, square rooting, completing the square, and using the quadratic formula. If an equation is factorable, all
of complex and abstract mathematical models. Chapter 10 objective is to develop foundation to graph and solve quadratic equations (Larson, Boswell, Kanold & Stiff, 2007). Applicable California Common Core Content Standards for Mathematics are moderately vigor and requires students to: 1. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. (Common Core Standard A-SSE-3b) 2. Create equations in two or more variables to represent relationships
parabola becomes wider. The result was still too thin. The next function was: Y= -0.05(X-8)2+2.33 I changed -0.1 to -0.05. As a gets closer to 0 the parabola becomes wider. The result was still too thin. The next function was: Y= -0.03(X-8)2+2.33 I changed -0.05 to -0.03. As a gets closer to 0 the parabola becomes wider. The result was off centre to the left. The next function was: Y= -0.03(X-8.5)2+2.33 I changed -8 to -8.5. As b decreases
Examples 6 Matrices Examples Cont. 7 Set Theory 8 Set Theory Examples 9 Equations 10 Equations 11 Equation Examples 12 Functions 13 Functions Cont. 14 Function Examples 15 Function Examples Cont. 16 Matrices A matrix in mathematics is a rectangular array of mainly numbers that are arranged in rows and columns. All of the individual numbers in the matrix are called
Newton-Raphson method. Problem Statement Newton-Raphson method is of use when it comes to approximating the root or roots of an equation. For a normal quadratic equation there is a well known formula to find the roots. There is a formula to find the roots of a 3rd and fourth degree equation but it can be troubling to find those roots, but if the function f is a polynomial of the 5th degree there is no formula that can enable us to find the root...
Cubic equations were known since ancient times, even from the Babylonians. However they did not know how to solve all cubic equations. There are many mathematicians that attempted to solve this “impossible equation”. Scipione del Ferro in the 16th century, made progress on the cubic by figuring out how to solve a 3rd degree equation that lacks a 2nd degree. He passes the solution onto his student, Fiore, right on his deathbed. In 1535 Niccolò Tartaglia figures out how to solve x3+px2=q and later
has to do with numbers of course, but it goes in depth and discusses how numbers relate to one another. Euler committed much of his time to number theory concerning topics such as the Pell equation, Fermat’s Last Theorem, perfect numbers, and the quadratic reciprocity law. Euler developed a theorem that proved Fermat’s theorem and created a deep understanding of Fermat’s theorem by doing so. Euler did not only do work concerning theorems made by other mathematicians, he developed identities and equations
Finding roots of a function is often a task which faces mathematicians. For simple functions, such as linear ones, the task is simple. When functions become more complex, such as with cubic and quadratic functions, mathematicians call upon more convoluted methods of finding roots. For many functions, there exist formulas which allow us to find roots. The most common such formula is, perhaps, the quadratic formula. When functions reach a degree of five and higher, a convenient, root-finding formula
Abstract—This paper is a report on the mathematics and the mathematicians of The Renaissance. During this time period, many significant advancements in mathematics occurred in many areas of mathematics, including algebra, trigonometry, and calculus. Similarly, it was during this time, due to the impending need to learn the mathematics of intricately complex and rather precise calculation, in which the abacist came into existence. Noteworthy as well are the many mathematicians who apported the mathematical
I selected to do a small group math lesson. At this time of the year eighth graders are reviewing for Standardized Testing. One of the things they need practice on is their algebra skills, such as solving linear equations. The focus of this lesson was on solving linear equations with one variable. There are various standards that deal with solving equations, but for these students I narrowed it down to single-variable equations: Solve linear equations. The Alabama standard used from this lesson was
In this portfolio task I have investigated the patterns in the intersection of parabolas and various lines. I have formed a conjecture to find the value of D of the parabolas, which are intersected by 2 lines, of varying slopes and shown the proof of its validity. I have used the TI-84 graphic display calculator, the software Geoegebra and Microsoft Excel to do my calculations. I have even investigated the values of D, for polynomials of higher powers and tried to come up with a general solution
The Function of Symbolism in Gabriel Garcia Marquez's 'A Very Old Man with Enormous Wings' In Gabriel Garcia Marquez's "A Very Old Man with Enormous Wings" an angel symbolizes the unfamiliar. The angel is not just a celestial body, but a foreign body-someone who stands out as being different from the rest of society. Consequently, the angel draws attention to civilized society's reaction, ergo the community's reaction within the story when it confronts him. Using the angel as a symbol, Marquez
The Scarlet Ibis by James Hurst Foreshadowing, symbolism, and image are all elements which compose style. All are very important; foreshadowing adds suspense, and symbolism contributes to interpretation. Image contributes "visual aids" which, also, aid interpretation. In this classic short story, "The Scarlet Ibis," by James Hurst, foreshadowing, symbolism, and image combine to create a true literary masterpiece. Foreshadowing is one of the elements of style which make "The Scarlet Ibis"
Functions of festivals in Early Modern Europe 'What were the functions of popular festivals, etc. in Early Modern Europe? And why did the authorities, civil and ecclesiastical seek to control or suppress them?' In Early Modern Europe festivals were the setting for heroes and their stories, to be celebrated by the populace. They posed a change from their everyday life. In those days people lived in remembrance of one festival and in expectance of the next. Different kinds of festivals were celebrated
I-Function, Pain And Memory Pain is capable of leaving a long lasting effect on ones life and in ones memory. It can literally "change" who "you" are. "You" change according to the input that your nervous system receives and reacts to. Permanent changes can be seen in long-term memories with the manufacturing of new proteins stored in the memory that account for the inputs. Pain can be an extremely powerful input to the nervous system with varying effects that could lay dormant for many years
Boundaries of the I-Function in Twins Identical, conjoined, and half-twins are all examples of intrinsic variability in humans. Intrinsic variability exists in all animals and is an adaptive mechanism built into the nervous system in response to input. This mechanism allows humans to distinguish the same inputs as different from one another and therefore, the possible outputs vary with time. It is possible that due to identical genetic input, the twins could share identical neural pathways and
Functional Areas of a Company Companies can achieve their corporative objectives only when the various functions of the company work together. There are four major functional areas in a company namely the MARKETING, FINANCE, HUMAN RESOURCES & PRODUCTION, but there are other businesses like Lewisham College that have other functional areas such as LEARNERS SERVICES & GENERAL STUDIES. All the functions set up their own objectives that want to achieve in accordance with the company’s objectives within
Roles and Functions of Law in Business and Society Introduction William O. Douglas said, "Common sense often makes good law." Well that is what laws essentially are, rules and regulations that make sure common sense is followed. One could even say that laws are enforced ethics. Laws serve several roles and functions in business and society, and this paper will discuss those roles and functions. What is law? According to Reference.com (2007), law is defined as: "rules of conduct of any organized
Tactics and marketing function audit Product (Customer benefits) Nike is focused on six product key categories: running, basketball, football, men’s training, women’s training and sportswear. Each category team is immersed in its sport’s culture, connecting with consumers and building deep relationships. Nike believes itself to be a premium brand, and they earn that reputation by delivering experiences that surpass the expectations of our consumers. Nike produces a wide range of sports equipment
Perspectives on Function and Use Function is often used in the usage or utility of something, but its meaning can be extended in many ways elucidated below. Architecture might function as a guideline for proper conduct in spheres of life. It may set and manipulate the rules by which people follow their lifestyle. Thus, the influence of architecture functioning as a change-maker in human behavior and moral principles can be traced to regions farther than its mere geographical presence. Vise versa