Answer to Question #147596 in Algebra for Amine

Question

Polynomial and rational functions can be used to model a wide variety of phenomena of science, technology, and everyday life.

Choose one of these sectors and give an example of a polynomial or rational function modeling a situation in that sector. [Hint: see the examples and exercises in the book.]

Go to www.desmos.com/calculator, write your equation, or function, and develop your explanation using the properties of graphs.

Answer 1

People use polynomials in their everyday life . People use polynomials for modeling of various buildings and objects , used in industries , used in construction . They are even used in marketing , finance , stocks . etc .

 the Legendre polynomials are used for the simulation of the scattering sound field in a multilayered elastic shells. an engineer designing a roller coaster would use polynomials to model the curves, while a civil engineer would use polynomials to design roads, buildings and other structures.

an example of polynomial and rational function

function f(x)= (3x-2)(x+2)²

y intecept =

f(0)= {3(0)-2}(0+2)²

= (-2)(4)

= -8

y intercept of the graph of y=f(x) is(0,-8)

x intercept

0= (3x-2)(x+2)²

3x-2=0 , x=2/3

(x+2)²=0 , x=-2

x intercepts of the graph of y=f(x) are (2/3,0) (-2,0).

Now find the end behaviour

f(x)= (3x-2)(x+2)²

f(x)= (3x-2)(x²+4x+4)

f(x) = 3x³+12x²+12x-2x²-8x-8

f(x) =3x³+10x²+4x-8

 the end behavior of function f will be the same as the end behavior of 3x³.

Now sketch the graph