1. Warm - Up Find the Vertex of f(x) = x 2 – 2x + 4

2. Announcements Assignment ▫p. 248 ▫# 25 - 28 ▫p. 291 # 1, 2, 15, 16, 21, 31, 32, 37, 38, 51, 52 Chapter Test 2.1 – 2.4 on Thursday. Corrections Friday if you have turned in all of your assignments

3. 2.4 Real Zeros of Polynomial Functions How to use the Rational Zero Test to determine possible rational zeros of polynomial functions How to use Descartes’s Rule of Signs

4. The rational zero test Any rational zero of f will be of the form p/q, ▫P = factor of the constant ▫Q = factor of the coefficient of term with highest degree ▫Possible rational zeros? f(x) = 2x 3 – x 2 + x + 4

5. Example 6. Find the possible rational zeros of f(x) = x 3 - 7x – 6 = 0. p:  1,  2,  3,  6 q:  1 p/q:  1,  2,  3,  6

6. How do we know which zeros will work?! Solve x 3 - 7x – 6 = 0. ▫p/q:  1,  2,  3,  6 Factor Theorem Evaluate the function at the possible rational zeros

7. Example 7. Find all real zeros of 3x 3 – 20x 2 + 23x + 10. p:  1,  2,  5,  10 q:  1,  3 p/q:  1,  2,  5,  10,  1/3,  2/3,  5/3,  10/3 One zero is 2. Two more come from solving using synthetic division

8. Example:Find the possible and real zeros of Rational Root Test:

9. Assignment Find all the possible zeros of the function 25) 2x 3 +3x 2 + 1 26) 2x 3 - 19x 2 + 33x – 9 27) 9x 4 - 9x 3 -58x 2 + 4x + 24 28) 2x 4 - 15x 3 + 23x 2 + 15x - 25