Yes, the STEELERS LOST yesterday!. Graphs of Polynomial Functions E.Q: What can we learn about a...
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Transcript of Yes, the STEELERS LOST yesterday!. Graphs of Polynomial Functions E.Q: What can we learn about a...
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Yes, the STEELERSLOST yesterday!
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Graphs of Polynomial Functions
E.Q: What can we learn about a polynomial from its graph?
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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
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Odd Polynomials One end of the graph falls One end of the graph rises
Does not matter what is in between
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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
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Even Polynomials The ends do the same thing They both either go up Or they both go down
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End Behavior Even polynomials: Both ends rise, and both
ends fall
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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
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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.
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Odd Polynomials Positive leading
coefficient Negative leading
coefficient
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Even Polynomials Positive leading
coefficient Negative leading
coefficient
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Even or Odd
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Even or Odd?
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Describe the end behavior of 3x7+5x+1040
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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
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What is the y intercept? 4x6+5x5+3x2+9
2x-9
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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
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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
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Find the zeros X3-2x2-5x+6
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Find the zeros X3+4x2-x-4
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Find the zeros X3+4x2-x-4