Answer to Question #147037 in Algebra for Patric

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

In engineering polynomial functions is used in designing a roller coaster to model the curves.

In civil engineering polynomials are used to design roads, buildings and etc.

Example of a polynomial used in civil engineering to model roads f(x)=(3x-2)(x+2)²

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.

Sketch above