Applications Of Polynomial Functions p3a4c

Applications Of Polynomial Functions BY: SHINA TAKADA

Definition: A polynomial function is a function such as a quadratic, a cubic, a quartic, and so on, involving only non-negative integer powers of x. We can give a general definition of a polynomial, and define its degree.

Applications Of Polynomials Functions and Many its Everyday Use: of us don't realize it, people in all sorts of professions use polynomials every day. The most obvious of these are mathematicians, but they can also be used in fields ranging from construction to meteorology. Although polynomials offer limited information, they can be used in more sophisticated analyses to retrieve more data.

How Do We Use Polynomials??  Engineers

use polynomials to graph the curves of roller coasters

 Since

polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example.

Polynomials in Modeling or Physics:  Polynomials can also be used to model different situations, like in the stock market to see how prices will vary over time. Business people also use polynomials to model markets, as in to see how raising the price of a good will affect its sales. Additionally, polynomials are used in physics to describe the trajectory of projectiles. Polynomial integrals (the sums of many polynomials) can be used to express energy, inertia and voltage difference, to name a few applications

Polynomials in our Industry:  For

people who work in industries that deal with physical phenomena or modeling situations for the future, polynomials come in handy every day. These include everyone from engineers to businessmen. For the rest of us, they are less apparent but we still probably use them to predict how changing one factor in our lives may affect another without even realizing it.

Example Of Uses 1:  The

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stock market. (price vs. time)

Water levels in a resevoir. (height vs. time)

Examples  Demand

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for electricity. (watts vs. time)

The curves of a scalable computer font. (y vs. x)

Real Life Problem: 

Let's say you have a square piece of sheet aluminum that is 12 inches on each side. You want to cut a square of dimension x by x from each corner of the sheet and then fold the sides up to make an open topped box. What dimension should you select for x so that box you make has the maximum possible volume?

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If the original sheet of metal is 12" by 12", and you cut an x by x square from each corner, the dimensions of the bottom of the box would then be 12 - 2x inches. Then the volume with respect to the x dimension of the box would be

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V(x)=(12 – 2x) . X

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First, let's test a couple of values to see if it makes any difference. Let's try x = 1. x = 1 means that our box would be 10 by 10 on the bottom and 1 inch tall for a total volume of 100 cubic inches. Let's try x = 3. x = 3 means that the box would be 6 by 6 on the bottom and 3 inches tall, 6 X 6 X 3 = 108 cubic inches. So clearly the selected value for x makes a difference in the volume.

Real Life Problem 

V (x) = 4x3 – 482+144x (PS, Tito rex, it’s four and 3 squared and the other one is 48 squared) the polynomial function, and the real life problem would be to find the value of x that makes the volume a maximum.

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(Ps: Tito Rex I made the graph at photoshop so please

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Excuse if it sucks)

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The graph illustrates the situation. Values for x larger than 6 don't have any application because if x were 6 or larger, there wouldn't be any metal left to make a box. So the interval of interest is 0 <x<6