Yes, the STEELERSLOST yesterday!

Graphs of Polynomial Functions

E.Q: What can we learn about a polynomial from its graph?

Odd and Even Polynomials Odd polynomials- highest exponent is odd

(1,3, 5, 7) Even polynomials- highest exponent is even

(2, 4, 6) Even or Odd?

X3+2x2+4 X2+6x+9 2x-3 4x5+6x2

Odd Polynomials One end of the graph falls One end of the graph rises

Does not matter what is in between

End Behavior The end behavior of the graph of the

polynomial is the same as the end behavior of the graph of the leading term or highest exponent.

Look at the very ends of the graph to determine

Odd polynomials: One side of the graph rises, and one side of the graph falls

Even Polynomials The ends do the same thing They both either go up Or they both go down

End Behavior Even polynomials: Both ends rise, and both

ends fall

Leading Coefficient The number in front of the highest exponent is

the leading coefficient The number itself does not matter Need to determine if it is positive or negative Changes the end behavior

End Behavior Even numbered polynomials have end

behavior where both ends of the graph either go up, or both ends of the graph go down

Odd numbered polynomials have end behavior where one end of the graph goes up, and one end of the graph goes down.

Odd Polynomials Positive leading

coefficient Negative leading

coefficient

Even Polynomials Positive leading

coefficient Negative leading

coefficient

Even or Odd

Even or Odd?

Describe the end behavior of 3x7+5x+1040

Intercepts For any polynomial function

Y intercept is the constant term in the equation (the one without the x attached)

X intercepts are the real zeros of the polynomial (we will use the calculator to find them)

A polynomial will always have one y intercept

What is the y intercept? 4x6+5x5+3x2+9

2x-9

Zeros You can have as many zeros or x intercepts as

the degree of the polynomial Look at the highest exponent 2x5+4x3-6x+1 could have how many x

intercepts?

Cannot have any more than the highest exponent, but does not have to have that many x intercepts

Locating Zeros using the calculator Plug the polynomial function into y= on the

calculator Graph Make sure your graph looks OK Go to second graph Brings up a table Look at the table for the values of x where

y=0

Find the zeros X3-2x2-5x+6

Find the zeros X3+4x2-x-4

Find the zeros X3+4x2-x-4