November 16, 2017

DO NOW!

1) Turn in ________ and take back your graded homework.

3) Sit quietly to facilitate a rapid start to class

The Thanksgiving Blues....

2) Take out last night's homework and raise your hand for a stamp

November 16, 2017

Today's Agenda:1) Homework Reminder

2) Update on next week

3) Correct 6.5

4) 6.6: Finding Rational Zeros

5) 6.6(Ext): Descartes' Rule of Signs

6.1 - 6.4 QuizNon-graphing calculator allowed on quiz

November 16, 2017

November 16, 2017

Next Week...

November 16, 2017

Review from yesterday:• Is (x+2) a zero of ?

How do we know?

November 16, 2017

Questions from last night's homework?

November 16, 2017

6.6: Date:

• I CAN find all zeros of a polynomial function

November 16, 2017

Two Important Theorems:

Factor Theorem:

Let f be a polynomial function. Then (x-c) is a factor of f(x) if and only if f(c)=0.

Theorem - Number of Zeros:

Corollary: A polynomial function may have fewer real zeros than its degree.

A polynomial function has exactly as many zeros as its degree.

November 16, 2017

Determining Possible Zeros:

Find all Real Zeros:

Where do we start?

Rational Zeros TheoremFor a polynomial function, the possible rational zeros can be found by writing all ratios

where p is a factor of the constant term (last term)and q is a factor of the leading coefficient.

List possible zeros of f(x):

November 16, 2017

Your turn: Determining Possible Zeros:

List all possible Zeros:

November 16, 2017

At your table:

Find all Real Zeros:Steps:

Check your answer by graphing!

November 16, 2017

Your chance to learn more about your classmates!

Who is __________?We will ask question until the timer ends. Be creative!

Ground Rules:- Inappropriate questions will end the activity. Act responsibly so we can all enjoy the opportunity to get to know each other!

VIPSpotlight

November 16, 2017

Can we make this any easier? Yes!!• Descartes' Rule of Signs:

The number of positive real zeros of f(x) equals the number of sign changes in the coefficients of f(x) OR that number minus an even integer.

The number of negative real zeros of f(x) equals the number of sign changes in the coefficients of f(-x) OR that number minus an even integer.

November 16, 2017

Let's apply Descartes' Rule of Signs!

List all possible zero combinations:

November 16, 2017

Putting it all together: Question revisited:Find all Real Zeros:Steps:

November 16, 2017

Homework Time!• You may work alone or with the other members of

your table• Use your time Productively!

November 16, 2017

Concept Check:

Today we learned....

1) How to find all zeros of a polynomial

2) How to use Descartes' Rule of Signs to determine possible zeros of a polynomial

Update Your Assignment Sheet with Tonight's Homework:

Section 6.6 Assignment

Descarte's Rule of Signs Worksheet - Answer Key on Class Website

Extra Credit Quiz Review (2 parts) - Answer Key on Class Website

Assigned: __________ Stamped: _________ Due: __________