1. 4-5 Exploring Polynomial Functions Locating Zeros

2. Graphing Polynomial Functions and Approximating Zeros Look back in Chapter 4 to help with understanding finding zeros and the definition of even and odd functions Location Principle: –If y = f(x) is a polynomial function and you have a and b such that f(a) 0 then there will be some number in between a and b that is a zero of the function A relative maximum is the highest point between two zeros and a relative minimum is the lowest point between two zeros a b zero

3. Let’s use the table function on the graphing calculators combined with what we know about possible zeros. Graph the function f(x) = -2x 3 – 5x 2 + 3x + 2 and approximate the real zeros. There are zeros at approximately -2.9, -0.4, and -0.8.

4. Upper Bound Theorem If p(x) is divided by x – c and there are no sign changes in the quotient or remainder, then c is upper bound

5. . Lower Bound Theorem If p(x) is divided by x + c and there are alternating sign changes in the quotient and the remainder, then -c is the lower bound.

6. Let’s put them to use… Find an integral upper and lower bound of the zeros of