Graphing Polynomials

• Determine degree– End behavior– Number of Zeros – Turning points

• Find the zeros and determine behavior at zero• Find the y-intercept and a few other points

The end behavior of a polynomial function’s graph is the behavior of the graph as x approaches infinity (+ ) or negative infinity (– ). The expressionx + is read as “x approaches positive infinity.”

END BEHAVIOR

What we already know

• Think about the end behavior of the following

2

2

3 2

2 1

7

2 3

y x

y x

y x

y x

Let’s Explore• Consider the following functions.

3 24 6f x x x x 3 22 3 5 6g x x x x

• Degree3

• Leading Coefficient1

• Degree3

• Leading Coefficient-2

Let’s Explore• Consider the following functions.

4 3 23 2 5 2 1f x x x x x 4 3 22 3 5 1g x x x x x

• Degree4

• Leading Coefficient-3

• Degree4

• Leading Coefficient1

END BEHAVIOR

END BEHAVIOR FOR POLYNOMIAL FUNCTIONSCONCEPT

SUMMARY

> 0 even f (x) + f (x) +

> 0 odd f (x) – f (x) +

< 0 even f (x) – f (x) –

< 0 odd f (x) + f (x) –

LC deg x – x +

HOMEWORK 11/15

PAGE 354-356, 1-18 all,

x+3 is a factor of this polynomials. Graph the polynomial.

MULTIPLICITY

3 2 5 3f x x x x