Warm-Up

State an equation for the following polynomial:

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

x

y

Polynomial Graphing Pt. 2

Learning Targets

End Behavior

Turns or “Bumps” for each polynomial

Investigate Roots

End Behavior

Leading Coefficient Degree End Behaviors

Positive

Negative

Positive

Negative

End BehaviorDegree

Even

Even

Odd

Odd

Types of Roots

Polynomial solutions are made up of complex roots

A root is where the polynomial’s graph will intersect with the x-axis

A complex root describes two different types of roots:› Real Roots› Imaginary Roots (we will get to these next

week)

Root Classifications

We classify the type of Real Root based on the degrees of each term and how it interacts with the x-axis.

Types:› Single Root› Double Root› Triple Root› And so on…

Examples:

Single Rootsf(x)=(x-2)(x+2)

-4 -3 -2 -1 1 2 3 4

x

y

Examples:

Double Rootsf(x)=.05((x-2)^2)((x+2)^2)

-4 -3 -2 -1 1 2 3 4

x

y

Examples:

Triple Rootsf(x)=.05((x-2)^3)((x+2)^3)

-4 -3 -2 -1 1 2 3 4

x

y

You Try

Classify each type of root:

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

x

y

Practice

Sketch the following polynomials, describe the end behavior and classify the roots:

1)

2)

3)

#1

-19-18-17-16-15-14-13-12-11-10-9-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 9101112131415161718192021

x

y

This is only a sketch

#2

-19-18-17-16-15-14-13-12-11-10-9-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 9101112131415161718192021

x

y

This is only a sketch

#3

-18-17-16-15-14-13-12-11-10-9-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 9101112131415161718192021

x

y

This is only a sketch

Turns In a Graph

What determines the number of turns the graph of a polynomial will have?

› End Behavior› Degree of the Leading Term› Degrees of each factor, or the types of roots

The maximum number of turns a polynomial can have is (n-1) where n is the degree of the leading term

For Tonight

On the worksheet from Thursday:› Describe the end behavior using the

correct math notation

› Circle each root on the graph.› Label each root as single, double or Triple.

http://www.wired.com/images_blogs/wiredscience/2013/10/600-grey-goblin.gif