5. We can use Quadratic functions to help predict Supply and demand
6. We can use Quadratic functions to predict future behavior
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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)
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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
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17. Did you know that quadratic equation is used to study growth of bacteria in an organism?
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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