Polynomial Functions

Polynomials are the building blocks of

Algebraic Modeling…

Lego is used to build cool models

Polynomials are used to build math models (also cool…)

Linear models have some value, but they are very basic…(y=mx + b)

Curves are very complex, and have unlimited potential for applications..

Curves

Found in the designs of bridges, buildings, vehicles, furniture, containers, jewelery, games, food, clothes, amusement parks, golf courses, art…

Careers as engineering, achitecture, graphics design, interior design, landscaping…

Sooooo….where do we start?How do we proceed?..

• Function notation and simple mechanics

A reminder of a Function… A function is a relationship between a set

of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

YES! NO!

Also, a function must pass the vertical line test.

Notation:

y = x2 + 3x + 7

“This is a function that is built using the variable x….”

“ f of x ”

f(x) = x2 + 3x + 7

This form is better for us when we operate

One of the most important uses of a model is that it can tell us

the value of the output at a specific input….

Think pay…

Given f(x) = 4x2 + 7x + 2, find f(5)

f(5) = 4(5)2 + 7(5) + 2

= 4(25) + 7(5) + 2

= 100 + 35 + 2

= 137