Introduction to polynomials, leading coefficients test, and zeros.

1. 2.2 Polynomial
Functions of Higher
Degree
Essential Question:
What is the leading coefficient test?
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2. Graphs of Polynomial Functions
Characteristics of a polynomial graph:
- __________ (no breaks, holes, or gaps)
- __________ (no sharp edges)
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3. What's a Power Function?
Even Odd
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4. Whiteboards!
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5. Transformations!
Ex. 1) Graph.
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6. Leading Coefficient Test
As x moves without bound __________ or
__________, the graph of the polynomial
function eventually ___________ or
__________ in the following manner:
n is _____:
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7. n is ______:
What does this mean?
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8. Rally Coach:
Describe the left and right hand behavior of the
function.
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9. Zeros of a Polynomial Function
Given f is a function of degree n:
Number of real zeros:
Number of turning points:
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10. Real Zeros of Polynomial Functions
If f is a polynomial function and a is a real number, the
following statements are equivalent:
1) ________ is a _________ of the
function f.
2) ________ is a _________ of the
polynomial equation f(x) = 0.
3) ________ is a _________ of f(x).
4) ________ is an _____________ of
the graph of f.
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11. *** Add this below the Real Zeros Slide!
Repeated Zeros
A factor (x-a)k yields a repeated zero x = a
of ___________ k.
1) If k is ______, the graph _________
x-axis at x = a.
2) If k is ______, the graph _________
the x-axis at x = a
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12. Ex. 2) Find all real zeros of
Determine the number of turning points as well.
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13. Bonus Example!!
Ex. 3﴿ Find a 5th degree polynomial with
x=­3, 1, 5, and 6 as zeros.
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14. Assignment:
2.2A p. 148 #13-21
(odd), 27-41 (odd)
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