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4-5 Exploring Polynomial Functions Locating Zeros

4-5 Exploring Polynomial Functions Locating Zeros. 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 :

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4-5 Exploring Polynomial Functions Locating Zeros

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  1. 4-5Exploring Polynomial FunctionsLocating 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 and f(b) > 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 zero b

  3. Let’s use the table function on the graphing calculators combined with what we know about possible zeros. Graph the function f(x) = -2x3 – 5x2 + 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

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