1. Today in Pre-Calculus Go over homework Notes: (need calculator & book)
Graphs of Polynomial Functions
End Behavior
Zeros
Homework

2. End Behavior of Polynomial Functions
Page 203 Exploration 1
If degree of polynomial is odd
If degree of polynomial is even
If leading coefficient is negative: graph reflects over x-axis so the end behavior changes signs.

3. End Behavior of Polynomial Functions
Examples: Describe the end behavior of the following functions without graphing them.
1) f(x) = x3 + 2x2 – 11x – 12
2) g(x) =–2x4 + 2x3 – 22x2 – 18x + 35

4. Finding Zeros of Polynomial Functions
Example: Find the zeros of f(x) = 5x3 – 5x2 – 30x
5x3 – 5x2 – 30x = 0 set equal to zero
5x(x2 – x – 6) = 0 factor GCF
5x(x – 3)(x + 2) = 0 factor
5x = 0 x – 3 = 0 x + 2 = 0 set EVERY term = 0
x = 0, 3, solve for x

5. Multiplicity of a Zero
If f is a polynomial function and (x – c)m is a factor of f, then c is a zero of multiplicity m. (c is a repeated zero).
Example: f(x) = (x – 2)3(x+1)2
If the multiplicity is odd, then the graph crosses the x-axis at (c,0) and the value of f changes sign at x = c
If the multiplicity is even, then the graph touches (but does not cross) the x-axis at (c,0) and the value of f does NOT change sign at x = c

6. Homework
Pg. 209: 9-12, 26-28, 34, 36, 39-41
Quiz: Tuesday, October 30