 Yes, the STEELERS LOST yesterday!. Graphs of Polynomial Functions E.Q: What can we learn about a polynomial from its graph?

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Presentation transcript:

 Yes, the STEELERS LOST 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?  X 3 +2x 2 +4  X 2 +6x+9  2x-3  4x 5 +6x 2

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 3x 7 +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?  4x 6 +5x 5 +3x 2 +9  2x-9

Zeros  You can have as many zeros or x intercepts as the degree of the polynomial  Look at the highest exponent  2x 5 +4x 3 -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  X 3 -2x 2 -5x+6

Find the zeros  X 3 +4x 2 -x-4

Find the zeros  X 3 +4x 2 -x-4