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Polynomials Functions & Rollercoasters
Transcript of Polynomials Functions & Rollercoasters
The “coaster” part was made out of blocks of ice with seats carved onto it, and the seats were filled with straw for insulation.
The sleds would slide down a 70 ft wooden frame (which was packed with snow and water to form ice).
There was sand at the end of the frames to slow down the sleds.
At the end, the workers would have to drag the sleds back to the top of the mountain. For example... Brief Introduction It is quite common for roller coasters to have parabolic shapes. These shapes can only be made using polynomials. For example, if you were to graph x^2 + 6x + 9, you'd get a parabola shape no matter what numbers you replace x with. Therefore, you need to use polynomials in order to get those parabolic shapes on roller coasters. Polynomial Functions What is it? Why Polynomials? ROLLER COASTERS Polynomial Functions & If you were to graph the expression: You would get the shape of a roller coaster: The number of max/min points is 1 less than the degree of any equation * An algebraic expression which contains one or more terms
* Polynomial functions are expressed in the form: n = a whole # a = a real # the coeff. of the greatest power of x, is the leading coeff. the coeff. with a 0, is the constant term x = variable * We were interested in figuring out what the mechanics behind roller coasters were, we then realized that polynomial functions were used to design roller coasters Why we found this topic interesting; History of Polynomials: * The word “algebra” was derived from the Arabic word for restoration, AL-jabru
* Islamic mathematicians were able to;
~ solve basic algebra of polynomials
~ the ability to multiply
~ divide and find square roots of polynomials
~ and had much knowledge of the binomial theorem during the medieval times Diophantus Hero of Alexandria Isaac Newton Leonardo Fibbonacci Carl Friedrich Gauss Let's look at an example: The shape of a roller coaster can be modeled by the equation: Let's take the equation for example. If we graphed this equation, it would look like this: The graph contains all the different components such as:
* an analysis of the graph using the leading coefficient (whether its positive or negative)
* local maximums and minimums
* absolute maximums and minimums
* turning points
* whether the function is odd or even based on the degree
* the basic principles of graphing
* the end behaviors of a function Key Features Video: The End :) ~ once we chose our math topic, polynomials, we found an immediate connection to roller coasters ~ ~ roller coasters imitate the shape of polynomial functions, we realized that we could connect those two
~ it included concepts that we were comfortable with: use of simple algebraic strategies, AROC, IROC, and listing the key features of a graph For example, for this equation the number of max/min points would be: .... 6 The graph would look like this;