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Warm-Up: November 27, 2012

Warm-Up: November 27, 2012. Solve x 3 +2x 2 -2x-1=0. Homework Questions?. Zeros of Polynomial Functions. Section 7.5. Essential Question. How can we find every zero of a polynomial function?. Improved Guess and Check. There are a limited number of possible rational roots of a polynomial.

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Warm-Up: November 27, 2012

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  1. Warm-Up: November 27, 2012 • Solve x3+2x2-2x-1=0

  2. Homework Questions?

  3. Zeros of Polynomial Functions Section 7.5

  4. Essential Question • How can we find every zero of a polynomial function?

  5. Improved Guess and Check • There are a limited number of possible rational roots of a polynomial. • Write down all the factors of the constant term. • Write down all the factors of the leading coefficient. • Any rational root must be of the form • This is called the Rational Root Theorem.

  6. Example 1 • Find all roots of

  7. You-Try #1 • Find all roots of

  8. Reminder • All of the following mean basically the same thing: • Root • Zero • X-intercept • Solutions • They all mean “solve for x”

  9. Extra Step for Finding Zeros • First replace f(x) with 0 • Then solve for x

  10. Example 2 • Find all the zeros of

  11. You-Try #2 • Find all the zeros of

  12. Assignment • Page 464 #11-25 odd • Bring your graphing calculator to class every day (especially tomorrow)

  13. Warm-Up: November 28, 2012 • Simplify each of the following

  14. Homework Questions?

  15. Continuing 7.5 notes

  16. Reminder • All of the following mean basically the same thing: • Root • Zero • X-intercept • Solutions • They all mean “solve for x”

  17. Extra Step for Finding Zeros • First replace f(x) with 0 • Then solve for x

  18. Example 3 • Find all the zeros of

  19. Warm-Up: November 29, 2012 • Use the quadratic formula to find the zeros of

  20. Finding Zeros on TI-83

  21. You-Try #3 • Find all the zeros of

  22. Multiplicity • If (x-r) is a factor that occurs m times in the factorization of a polynomial, then r is a root with multiplicitym. • If m is even, the graph will touch but not cross the x-axis at r. • If m is odd, the graph will cross the x-axis at r.

  23. Example 5 • Write a polynomial function, P, in factored form and in standard form by using the given information:

  24. You-Try #5 • Write a polynomial function, P, in factored form and in standard form by using the given information:

  25. Warm-Up: November 30, 2012 • Find all zeros of

  26. Continuing 7.5 Notes

  27. Complex Conjugate Root Theorem • If is a root/zero, then must also be a root/zero.

  28. Example 6 • Write a polynomial function, P, in factored form and in standard form by using the given information:

  29. You-Try #6 • Write a polynomial function, P, in factored form and in standard form by using the given information:

  30. Assignment • Page 464 #27-33 odd, 41-49 odd

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