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Polynomials and Roller Coasters - Math project
Transcript of Polynomials and Roller Coasters - Math project
History of Roller Coasters
Polynomials are everywhere. They play a key role in the study of algebra, in analysis (e.g Taylor series), and on the whole many mathematical problems involve them, if not in the answer then at least in a part of the solution.
Roller coasters imitate the shape of a polynomial functions For example, it's quite common for roller coasters to take the shape of a parabola.
In mathematics, a polynomial is an expression consisting of variables, called indeterminates, and coefficients that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. An example of a polynomial of a single indeterminate (or variable), x, is x2 − 4x + 7, which is a quadratic polynomial.
The origin of the Roller Coaster dates back to the Russian Ice Slides built in the 17th century. They began in the "Russian Mountains" in St. Petersburg Russia.
An expression of more than two algebraic terms
Polynomial functions are expressed in the form :
The leading coefficient is the power of the x.
a is real #
n = a whole #
x = variable
0 is constant term.
Carl Friedrich Gauss
Hero of Alexandria
The structures were built out of lumber with a sheet of ice several inches thick covering the surface. Riders climbed the stairs attached to the back of the slide, sped down the 50 degree drop and ascend the stairs of the slide that laid parallel to the first one. The slides were very popular with the Russian upper class, and some were elegantly decorated to provide entertainment "fit for royalty."
The first looping coaster was located in Frascati Gardens in Paris, France. The hill was 43 feet high, had a 13 foot-wide loop and was tested with everything under the sun before humans were allowed on. The layout was simple: the rider rode down the gentle slope on a small cart and through a small metal circle.
Example , Lets see this Equation :
Its will be look like this :
What is it polynomials ?
Done by =)
1- Alia Ahmed
2- Aisha Ahmed
3- Alyazia Rashid
4- Fatima Moh'd
The Equation :
The standard Formula :
The definition of a polynomial is: a function P(x) represented as for a natural n.
End behavior :
History of Polynomial
The equation we used :
The graph :
Long division :
Synthetic Division :