Teampresentation4

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Quadratic functions are useful in everyday situations like business and predicting supply and demand. They can be expressed as an equation in the form y=ax^2+bx+c, where a≠0. The earliest evidence of quadratic equations was found on clay tablets from ancient Babylon dating back to 1800-1600 BC. Quadratic functions are used today in many areas including calculating vehicle speeds and stopping distances, playing sports, weather prediction, and modeling how objects move under gravity.

Technology Education

Project Overview and Objectives ,[object Object]

Explain how quadratic functions work in every day uses.

Give examples of quadratic functions in every day uses,[object Object]

We can use Quadratic functions to help predict Supply and demand

We can use Quadratic functions to predict future behavior

We can use Quadratic functions to help maximize profits ,[object Object]

History Of Quadratic Functions ,[object Object]

The earliest evidence of quadratic equations were found on clay tablets in ancient Babylon during the 1800 BC to 1600 BC. Also on these tablets, it gave the early method for answering the problems.(http://www.mytutoronline.com/history-of-quadratic-equation,n.d.),[object Object]

Basics of Quadratic Equations The basic use of a quadratic equation is to find the curve on a Cartesian grid. The primary use is to find the curve that objects take when flying through the air. It is also used to design any object that has a curve and any specific curved shape needed for a project. (http://www.mathworksheetscenter.com/mathtips/linearequations.htmln.d)

Interesting Facts About Quadratic Equations We owe the Babylonians, the modern idea of angles, including the way a circle is divided up into 360 degrees. We also owe them for the not so pleasant invention of the taxman. (Budd &Sangwin, 101 uses of Quadratic Equations, 2004)

More Interesting Facts About Quadratic Equations Newton, who worked in optics, discovered using mirrors in telescopes instead of lenses in order to bring all points into focus. This was done through the use of mirrors in the shape of parabola. (Budd &Sangwin, 101 uses of Quadratic Equations, 2004)

Other Ways in Which Quadratic Equations are Used ,[object Object]

Quadratic Equations are used by car makers to determine how much and what type of breaks are needed to stop a car from going at various speeds

Police officer investigates a car accident scene to determine what velocities the cars were traveling when the collision occurred (www. mathworksheetcenter.com,n.d.),[object Object]

This document discusses using computer vision and simulation for object tracking. It outlines using the Hough transform circle algorithm and smallest circle algorithm to detect circles in an image. The detected circles are then fed into a robot simulation to track an object of interest. The simulation displays a box representing a robot that follows the tracked object at a fixed velocity while allowing the turning velocity to be adjusted. Image processing and simulation are run on separate threads for efficiency. Improvements proposed include background subtraction, using OpenCL for multicore processing, adding more variables to the simulation, and implementing a real-time operating system.

Role of theory in data analytics

Scott Mikalauskis

The document discusses the value of combining data analytics with theoretical frameworks. It provides examples of how theory can help uncover deeper insights and secrets that are invisible to predictive analytics alone. Specifically, it discusses how theory helped reveal there must be two ways for calcium ions to exit photoreceptor cells, leading to new discoveries. It also discusses how economic and physical theories can be combined with data to model how disturbances in complex transportation networks propagate and have far-reaching effects. The overall message is that while analytics is powerful, combining it with applicable theories yields even greater insights and predictive capabilities.

Pre-Cal 40S March 9, 2009

Darren Kuropatwa

Geometric Transformations I

Kasun Ranga Wijeweera

This document discusses 2D geometric transformations including translation, scaling, and rotation. Translation moves an object by adding offsets tx and ty to the x and y coordinates. Scaling enlarges or shrinks an object by multiplying the x and y coordinates by scaling factors sx and sy. Rotation rotates an object around the origin by an angle θ, with the new x and y coordinates calculated using trigonometric functions of the original point coordinates and θ.

A25.8 modelingquads

vhiggins1

This document provides instructions for writing quadratic equations given different conditions: 1) Given the vertex and another point, use the vertex form and plug in the points to solve for coefficients. 2) Given the x-intercepts and another point, write the x-intercepts as factors and use the other point to solve for the coefficient. 3) Given a data table of x and y values, find the quadratic model in standard form that best fits the data. Examples are provided for writing equations based on given points or intercepts.

Monte carlo

Azarium74

This document discusses Monte Carlo simulations. It provides an overview of Monte Carlo history and methods, including examples of applications. Monte Carlo simulations are stochastic computational algorithms that rely on repeated random sampling to obtain numerical results. They allow modeling complex systems without having to solve detailed deterministic equations. Some key advantages are that they are generally easy to parallelize and provide no dynamical information like molecular dynamics simulations.

Generalized Low Rank Models

Sri Ambati

This document discusses generalized low rank models, which provide a compressed representation of data tables by approximating them as the product of two smaller numeric tables. This reduces storage space and improves prediction speed while maintaining accuracy. Two examples are described: one where low rank models are used to visualize important stances from walking data, and another where they compress zip code data to predict compliance violations.

H2O World - GLRM - Anqi Fu

Sri Ambati

Generalized low rank models provide a compressed representation of data by identifying important features and representing each data point as a combination of those features. This reduces storage space, speeds up predictions, and helps visualize patterns in the data. Examples show how low rank models can compress walking stance data to identify principal poses and compress zip code data into demographic archetypes to improve compliance predictions across regions.

Calculus I Directions: (10 pts. each) Answer each of the following questions below. In order to receive ANY credit for a question, you must SHOW YOUR WORK using proper notation and clear and concise logic. You're graded on both the accuracy of your answers AND your explanations that sufficiently support your answers. Unless otherwise stated, you're to give the EXAXCT VALUES of answers instead of decimal approximations. In order to receive ANY credit for any applied/word problem (i.e. Problems #29 - ), you MUST declare a variable (unless the variable(s) have already been declared in the problem) and set up and solve an appropriate mathematical expression that can be used to answer the question. Proper units must also be included in answers to applied problems. NO CREDIT WILL BE GIVEN FOR EITHER GUESSING OR CHECKING POSSIBLE ANSWERS WITHOUT SOLVING THE PROBLEM. YOU CANNOT USE CALCULUS TO SOLVE THESE PROBLEMS. Finally, write ONLY FINAL ANSWERS ON THESE PAGES; you must show your work both according to homework guidelines and on YOUR OWN PAPER. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Multiply or divide as indicated. Write your answer in factored form. 1) x22 - 9x + 14 · xx22 -- 1618x x ++ 4877 1) 2) x - 12 x + 32 Simplify the complex rational expression. 4 x 2 - 4 x - 32 - 1 x - 8 2) 1 + 1 x + 4 Find the difference quotient for the function and simplify it. 3) g(x) = 6x2 + 14x - 1 3) Find the domain and range of the function. Write your answers using interval notation. 4) g(z) = 16 - z 2 4) Find a formula for the function graphed. 5) 5) Determine if the function is even, odd, or neither. You must use algebra to justify your answer; otherwise, no full credit will be given. NO CREDIT is given for an answer without a mathematical explanation. 6) f(x) = x -+7 9 6) State the domain of the composition. 7) ( g H h)(x) with g(x) = x + 5 and h(x) = 8 x + 7 7) Compute f(x + h) - f(x) h (h J 0) for the given function . 8) f(x) = 4x - 8 8) 9) f(x) = 5 x 2 + 6 x 9) 10) f(x) = 1 9 x 10) Solve the equation by multiplying both sides by the LCD. 11) 32x - x 3+ 1 = 1 11) 12) Solve the equation. x + 6 + 2 - x = 4 12) 13) ( 4 x - 2 ) / 3 2 + 6 = 15 13) 14) 3 x + 4 = x - 1 14) Find the real solutions of the equation by factoring. 15) x3 + 8x2 - x - 8 = 0 15) Solve the equation by making an appropriate substitution. 16) (x2 - 2x)2 - 11(x2 - 2x) + 24 = 0 16) Solve the logarithmic equation. 17) log2(x + 7) + log2(x - 7) = 2 17) Solve the exponential equation. Express the solution set in terms of natural logarithms. 18) 4x + 4 = 52x + 5 18) Solve the inequality and express the solution in interval notation. 19) 7Ax - 1A L 2 19) Solve the inequality. Write your answer using interval notation. 20) x 18- 5 > x 15+ 1 20) Write the equation as f(x) = a(x - h)2 + k. Identify the vertex, range, and axis of symmetry of the function. 21) f(x) = x2 + 5x + 2 21) 23) log F.

differentiation (1).pptx

Alpa Rajput

This document provides an overview of differentiation and derivatives. It defines the derivative as the instantaneous rate of change of a quantity with respect to another. The process of finding derivatives is called differentiation. Isaac Newton and Gottfried Leibniz developed the fundamental theorem of calculus in the 17th century. Derivatives have many applications across various sciences such as physics, biology, economics, and chemistry. They are used to calculate velocity, acceleration, population growth rates, marginal costs/revenues, reaction rates, and more.

Modeling and Reasoning in Event Calculus using Goal-Directed Constraint Answe...

Universidad Rey Juan Carlos

Automated commonsense reasoning (CR) is essential for building human-like AI systems featuring, for example, explainable AI. Event calculus (EC) is a family of formalisms that model CR with a sound, logical basis. Previous attempts to mechanize reasoning using EC faced difficulties in the treatment of the continuous change in dense domains (e.g. time and other physical quantities), constraints among variables, default negation, and the uniform application of different inference methods, among others. We propose the use of s(CASP), a query-driven, top-down execution model for Predicate Answer Set Programming with Constraints, to model and reason using EC. We show how EC scenarios can be naturally and directly encoded in s(CASP) and how it enables deductive and abductive reasoning tasks in domains featuring constraints involving both dense time and dense fluents.

Space Tug Rendezvous

Timothee de Mierry

This document summarizes an experiment that evaluated the efficiency of three search strategies for autonomous rendezvous in space: random, semi-autonomous, and autonomous. The experiment used LEGO robots to simulate a space tug searching for a target in a two-dimensional space, and measured the time and energy required for each strategy. It was found that the semi-autonomous strategy was most energy efficient but most time-consuming, while the autonomous strategy proved most suitable for space applications by being both reasonably energy efficient and faster. The results provide insight into optimal search algorithms for an actual space tug vehicle to implement during rendezvous and docking.

Differentiation of application

Md. Musfiqur Rahman Foysal

Differentiation allows us to find the rate of change of one variable with respect to another. Calculus helped improve navigation by providing a better understanding of how celestial bodies move. Differentiation and integration can help solve real-world problems like determining maximum/minimum values, finding tangents and normals, solving equations using Newton's method, optimizing costs/profits, and determining radii of curvature. The presentation concludes with information on increasing/decreasing functions and the nature of stationary points.

SSII2018企画: センシングデバイスの多様化と空間モデリングの未来

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This document summarizes a method for 4D reconstruction of crop fields using images collected over time from aerial vehicles. The method uses structure from motion and multi-view stereo to reconstruct 3D point clouds of the field for different time points. It then employs a spatio-temporal model and robust data association to align these reconstructions into a unified 4D model that captures how the crops change over time. The performance of the method is evaluated on a new dataset collected over a peanut field with ground truth measurements. Results show the 4D reconstructions qualitatively capture visual appearance changes and are quantitatively accurate for measuring crop geometric properties over time.

Algebra Inquiry.pptx

WillS36

This document outlines an inquiry into decision-making models and their use of relationships. It discusses key concepts in algebra like linear, nonlinear and cubic functions. A concept map shows relationships between algebraic concepts. The document proposes investigating cubic roots and their real-world applications, including hyperbolas. It connects algebraic concepts like parabolas, circles, and hyperbolas to the Victorian curriculum and potential applications in physics, engineering, and architecture.

Complex integration its uses and types

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Quadratic Function by Taylor & Asia

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Finding the Extreme Values with some Application of Derivatives

ijtsrd

There are many different way of mathematics rules. Among them, we express finding the extreme values for the optimization problems that changes in the particle life with the derivatives. The derivative is the exact rate at which one quantity changes with respect to another. And them, we can compute the profit and loss of a process that a company or a system. Variety of optimization problems are solved by using derivatives. There were use derivatives to find the extreme values of functions, to determine and analyze the shape of graphs and to find numerically where a function equals zero. Kyi Sint | Kay Thi Win "Finding the Extreme Values with some Application of Derivatives" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29347.pdf Paper URL: https://www.ijtsrd.com/mathemetics/other/29347/finding-the-extreme-values-with-some-application-of-derivatives/kyi-sint

Functional Systems @ Twitter

C4Media

Video and slides synchronized, mp3 and slide download available at URL http://bit.ly/1FKWssS. Marius Eriksen explains Twitter's experiences with functional programming (with Scala) @ Twitter: where functional techniques worked and where not. Also: how the Scala language has scaled with Twitter. Filmed at qconsf.com. Marius Eriksen is a Principal Engineer in Twitter's systems infrastructure group. His interests include large-scale distributed systems, storage systems, indexing systems, data management, distributed coordination, runtimes, profiling tools, networks, network protocols, and functional programming.

Calculus

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This document discusses derivatives, including their definition, history, real-life applications, and use in various sciences. Derivatives are defined as the instantaneous rate of change of one variable with respect to another and geometrically as the slope of a curve at a point. Their modern conception is credited to Isaac Newton and Gottfried Leibniz in the 17th century. Derivatives have applications in business for estimating profits and losses, and in automobiles to calculate speed and distance traveled from odometer and speedometer readings. They are also used in physics to define velocity and acceleration and in mathematics to study extreme values, mean value theorems, and curve sketching.

Quadcopter Design for Payload Delivery

Onyebuchi nosiri

Abstract This paper presents the design and implementation of a quadcopter capable of payload delivery. A quadcopter is a unique unmanned aerial vehicle which has the capability of vertical take-off and landing. In this design, the quadcopter was controlled wirelessly from a ground control station using radio frequency. It was modeled mathematically considering its attitude and altitude, and a simulation carried out in MATLAB by designing a proportional Integral Derivative (PID) controller was applied to a mathematical model. The PID controller parameters were then applied to the real system. Finally, the output of the simulation and the prototype were compared both in the presence and absence of disturbances. The results showed that the quadcopter was stable and able to compensate for the external disturbances.

Quadcopter Design for Payload Delivery

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Lab 2Lab 2- Kinematics.pdf142017 Lab 2 Kinematicsh.docx

smile790243

Lab 2/Lab 2- Kinematics.pdf 1/4/2017 Lab 2: Kinematics https://moodle.straighterline.com/pluginfile.php/72219/mod_resource/content/17/CourseRoot/html/lab004s001.html 1/20 Learning Objec뙕ves Disᣊ�nguish between scalar and vector quanᣊ�ᣊ�es Apply kinemaᣊ�c equaᣊ�ons to 1‐D and projecᣊ�le moᣊ�on Predict posiᣊ�on, velocity, and acceleraᣊ�on vs. ᣊ�me graphs Calculate average and instantaneous velocity or acceleraᣊ�on Determine that x and y components are independent of each other Relate velocity, radius, and ᣊ�me period to uniform circular moᣊ�on. Explain the direcᣊ�on of acceleraᣊ�on during uniform circular moᣊ�on 1‐D Kinema뙕cs 1‐D kinemaᣊ�cs occurs when an object travels in one dimension and can be described using words, equaᣊ�ons and graphs. Linear mo뙕on describes how an object will move horizontally or verᣊ�cally with constant acceleraᣊ�on, how an object will 1/4/2017 Lab 2: Kinematics https://moodle.straighterline.com/pluginfile.php/72219/mod_resource/content/17/CourseRoot/html/lab004s001.html 2/20 Figure 1: Pool balls in moᾷon demonstrate 1‐D kinemaᾷcs. Figure 2: Line secant to the path of the object. travel if dropped from the side of a cliff, and the path it will follow if thrown straight up into the air. Keep in mind the moᣊ�on of an object is relaᣊ�ve to the viewer. Even though you do not feel like you are in moᣊ�on right now, you are on planet earth that has rotaᣊ�onal moᣊ�on in addiᣊ�on to orbital moᣊ�on around the sun. In almost all cases here moᣊ�on will be relaᣊ�ve to the Earth. Scalar and Vector Quan뙕뙕es In physics, quanᣊ�ᣊ�es can be scalar or vector. The difference between the two lies in direcᣊ�on. Scalar quanᣊ�ᣊ�es include magnitudes, which are numerical measurements. The distance an object has traveled or the speed of an object is a scalar quanᣊ�ty. Scalars do not take direcᣊ�on into consideraᣊ�on and can be described with only a number and a unit. For example, somebody might say the temperature outside is 70°F. Seventy is the magnitude, and Fahrenheit is the unit; there is no direcᣊ�on associated with the quanᣊ�ty. Vector quanᣊ�ᣊ�es, on the other hand, include magnitude and direcᣊ�on. The displacement from an object's iniᣊ�al posiᣊ�on, velocity, and acceleraᣊ�on are vector quanᣊ�ᣊ�es. The direcᣊ�on of vectors can be described as being in the posiᣊ�ve direcᣊ�on, in the negaᣊ�ve direcᣊ�on, north, south, east, west, leĀ, right, up, down, etc. One might describe an airplane's velocity as 450 miles per hour due west where both magnitude and direcᣊ�on are given. It is important to disᣊ�nguish between scalar and vector quanᣊ�ᣊ�es when trying to understand kinemaᣊ�cs. Speed, Velocity, and Accelera뙕on You may be familiar with speed outside of the physics classroom. When you drive in a car you are traveling a distance over a certain amount of ᣊ�me: a speed. How then is velocity different from speed? Velocity (v) is a vector quanᣊ�ty described as the rate at which an object's posiᣊ�on changes divided by the ᣊ�me the ...

Atomic algorithm and the servers' s use to find the Hamiltonian cycles

IJERA Editor

Inspired by the movement of the particles in the atom, I demonstrated in [5] the existence of a polynomial algorithm of the order O(n 3 ) for finding Hamiltonian cycles in a graph with basis E= {x0,... , xn− 1 } . In this article I will give an improvement in space and in time of the algorithm says: we know that there exist several methods to find the Hamiltonian cycles such as the Monte Carlo method, Dynamic programming, or DNA computing. Unfortunately they are either expensive or slow to execute it. Hence the idea to use multiple servers to solve this problem : Each point xi in the graph will be considered as a server, and each server xi will communicate with each other server x j with which it is connected . And finally the server x0 will receive and display the Hamiltonian cycles if they exist

CFD_notes.pdf

Narayana Swamy G

The document discusses computational fluid dynamics (CFD) and the Navier-Stokes equations. CFD uses the Navier-Stokes equations, which are partial differential equations that describe the conservation of mass, momentum, and energy in fluid flow. The Navier-Stokes equations are derived from these conservation principles. They form a system of equations that can be discretized and solved using computers to simulate fluid flow. Key terms and concepts discussed include the continuity, momentum, and energy equations; equations of state; Newtonian fluids; and the compressible and incompressible forms of the Navier-Stokes equations.

Wiener Filter Hardware Realization

Sayan Chaudhuri

Super-resolution reconstruction is a method for reconstructing higher resolution images from a set of low resolution observations. The sub-pixel differences among different observations of the same scene allow to create higher resolution images with better quality. In the last thirty years, many methods for creating high resolution images have been proposed. However, hardware implementations of such methods are limited. Wiener filter design is one of the techniques we will use initially for this process. Wiener filter design involves matrix inversion. A novel method for the matrix inversion has been proposed in the report. QR decomposition will be the computational algorithm used using Givens Rotation.

Class 11 important questions for physics Scalars and Vectors

Infomatica Academy

An Efficient Convex Hull Algorithm for a Planer Set of Points

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This document presents an efficient convex hull algorithm for finding the convex hull of a planar set of points. The algorithm partitions the set of points into four regions based on the minimum and maximum x and y coordinates. It then finds the convex hull parts belonging to each region in parallel. Those parts are merged to derive the full convex hull. For each region, the algorithm uses a modified gradient concept to efficiently process the points and find the boundary points of the convex hull part. The algorithm achieves parallelism, data reduction, and has lower computational cost compared to traditional interior points algorithms. However, its drawbacks include difficulty extending it to higher dimensions and its static nature which requires the entire dataset from the beginning.

“Temporal Event Neural Networks: A More Efficient Alternative to the Transfor...

Edge AI and Vision Alliance

For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2024/06/temporal-event-neural-networks-a-more-efficient-alternative-to-the-transformer-a-presentation-from-brainchip/ Chris Jones, Director of Product Management at BrainChip , presents the “Temporal Event Neural Networks: A More Efficient Alternative to the Transformer” tutorial at the May 2024 Embedded Vision Summit. The expansion of AI services necessitates enhanced computational capabilities on edge devices. Temporal Event Neural Networks (TENNs), developed by BrainChip, represent a novel and highly efficient state-space network. TENNs demonstrate exceptional proficiency in handling multi-dimensional streaming data, facilitating advancements in object detection, action recognition, speech enhancement and language model/sequence generation. Through the utilization of polynomial-based continuous convolutions, TENNs streamline models, expedite training processes and significantly diminish memory requirements, achieving notable reductions of up to 50x in parameters and 5,000x in energy consumption compared to prevailing methodologies like transformers. Integration with BrainChip’s Akida neuromorphic hardware IP further enhances TENNs’ capabilities, enabling the realization of highly capable, portable and passively cooled edge devices. This presentation delves into the technical innovations underlying TENNs, presents real-world benchmarks, and elucidates how this cutting-edge approach is positioned to revolutionize edge AI across diverse applications.

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Mutation Testing for Task-Oriented Chatbots

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Conversational agents, or chatbots, are increasingly used to access all sorts of services using natural language. While open-domain chatbots - like ChatGPT - can converse on any topic, task-oriented chatbots - the focus of this paper - are designed for specific tasks, like booking a flight, obtaining customer support, or setting an appointment. Like any other software, task-oriented chatbots need to be properly tested, usually by defining and executing test scenarios (i.e., sequences of user-chatbot interactions). However, there is currently a lack of methods to quantify the completeness and strength of such test scenarios, which can lead to low-quality tests, and hence to buggy chatbots. To fill this gap, we propose adapting mutation testing (MuT) for task-oriented chatbots. To this end, we introduce a set of mutation operators that emulate faults in chatbot designs, an architecture that enables MuT on chatbots built using heterogeneous technologies, and a practical realisation as an Eclipse plugin. Moreover, we evaluate the applicability, effectiveness and efficiency of our approach on open-source chatbots, with promising results.

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Teampresentation4

1. Quadratic Functions

3. Explain how quadratic functions work in every day uses.

5. We can use Quadratic functions to help predict Supply and demand

6. We can use Quadratic functions to predict future behavior

10. Basics of Quadratic Equations The basic use of a quadratic equation is to find the curve on a Cartesian grid. The primary use is to find the curve that objects take when flying through the air. It is also used to design any object that has a curve and any specific curved shape needed for a project. (http://www.mathworksheetscenter.com/mathtips/linearequations.htmln.d)

11. Interesting Facts About Quadratic Equations We owe the Babylonians, the modern idea of angles, including the way a circle is divided up into 360 degrees. We also owe them for the not so pleasant invention of the taxman. (Budd &Sangwin, 101 uses of Quadratic Equations, 2004)

12. More Interesting Facts About Quadratic Equations Newton, who worked in optics, discovered using mirrors in telescopes instead of lenses in order to bring all points into focus. This was done through the use of mirrors in the shape of parabola. (Budd &Sangwin, 101 uses of Quadratic Equations, 2004)

13.

14. Quadratic Equations are used by car makers to determine how much and what type of breaks are needed to stop a car from going at various speeds

15.

16.

17. Did you know that quadratic equation is used to study growth of bacteria in an organism?

18.

19. Questions?

20. Resources Budd, C. and C. Sangwin. (May, 2004 1). 101 Uses of a Quadratic Equation. Retrieved June 26, 2011, from http://plus.maths.org/content/os/issue30/features/quadratic/index History of Quadratic equation and quadratic function retrieved from http://www.mytutoronline.com/history- of-quadratic-equation Media4mat (2008,Sept 23)Algebra Applications: Quadratic Functions [Video file] retrieved from http://www.youtube.com/watch?v=v-Z2-jxCqVw Online Etymology Dictionary retrieved from http://www.etymonline.com/index.php?term=quadratic Spector, L. (2001-2011). The Math Page. Retrieved from http://www.themathpage.com/alg/quadratic-equations.htm Stapel, Elizabeth. The Quadratic Formula Explained. Retrieved from http://www.purplemath.com/modules/quadform.htm Weisstein, Eric W. "Quadratic Equation." From MathWorld--A Wolfram Web Resource. Retrieved from http://mathworld.wolfram.com/QuadraticEquation.html Why Should We Care about Quadratic Equations (n.d.) retrieved from http://www.mathworksheetscenter.com/mathtips/quadraticequation.html

Editor's Notes

In our presentation we will explain where quadratic functions come from, what are some practical uses for quadratic functions . We will also give examples how different sectors such as businesses, and scientist use Quadratic functions in their respective field.
Businesses often use Quadratic functions to help figure out supply and demand, future behavior and how to maximize profits. Without these equations, businesses would not be able to run as smoothly or be profitable.
In this slide, we explain how a quadratic function can be expressed. We can solve the quadratic function by factoring, which we have done in the problem above. As you can see there are many steps that make up solving this equation.
Quadratic equations have been around for a very long time. Scientist found evidence of quadratic equations dating back to 1800 BC. Not only did the clay tablets have the problems on them, but it also had the solution and the work that showed the scientist how to answer the problem.
A parabola is a curve shaped like an arch. All points of a parabola have an equal distance fromthe focus, andthe directrix.The parabola opens up when a>0 and opens down when a<0.All parabolas have a line of symmetry meaning that if it gets folded in half, then it will match up exactly the same on both sides.
A Cartesian grid is a grid that shows just about any curve imaginable. The quadratic equation is able to draw that curve based on the data available for the given problem. The primary use of the quadratic equation is to find the exact curve that is created by an object that flies through the air such as a softball, tennis ball, football, baseball etc., along with things like aircraft, planets, vehicles in motion, artillery in the military and even sound waves from a speaker. Quadratic equations are used in just about every product in stores today. It is used to determine how safe the products are and the life expectancy of the products. They can then see what needs to be changed in order for the product to last longer.
The Babylonians had to figure out how to plant crops in a certain shape field in order to get the yield they needed to be able to pay the tax man and get what they also needed out of that field for food. The taxman back then were paid in crops for the taxes owed on the land. In order to figure this out the Babylonians used the a quadratic equation.
Newton recognized that Galileo’s telescopes were based on the use of lenses causing problems by refracting light of different colours in different ways. He fixed this problem by designing a telescope based on mirrors in parabola shapes to bring all points into focus.
By using geometrical arguments Newton was able to prove that such a law of force implied that the planets had to move around the sun in a conic section. (Of course, it was a tremendous fluke that the inverse square law led to orbits which could be explained in terms of known curves!) Another very important application is to find the stopping distance of a car travelling at a given velocity. A small reduction in speed leads to a much larger reduction in stopping distance. Solving the quadratic equation correctly here could, quite literally, save your, or someone else's, life
When a police officer investigates a car accident scene, he/she uses the quadratic equation in their efforts to determine what velocities the cars are traveling when the collision occurred. Also, who was at fault and why the vehicles were damaged the way they were. These calculations are also used by car designers to develop an even safer care for occupants during future collisions.
Scientists use a variety of quadratic formulas in various ways. One way is to figure out how time and distance relate to when objects move under gravity. Another way is studying growth of bacteria in organisms. Lastly but certainly not least they use quadratic equation to describe how planets move around the sun.
Quadratic equations are used in determining the stopping distance of vehicles. It also plays a part in determining how fast you need to travel to reach your destination in a certain amount of time.Playing sports such as tennis and bowling require the use of quadratic equations to determine the angle, speed and various other factors of the ball during game play.The electronic item we use everyday like tv’s, computers and cell phones require the use of quadratic equations to pick up signals so we can see the shows or hear the music.Weather predicating involves the use of quadratic equations to determine where a storm is move, how fast it is going and how much precipitation we will receive.Quadratic equations are used when figuring out taxes for the year, how much money we will have at retirement or how long it will take us to pay off a lone on a purchase.
Are there any questions?
We have provided links to resources used for our presentation for more information on Quadratic Equations please feel free to visit one or more of the sites listed.

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Editor's Notes