3. The “zero” of a function is just the value at which a function touches the x-axis.

4. It is easy to find the roots of a polynomial when it is in factored form! (x - 3) and (x + 5) are factors of the polynomial. Factored Polynomial

5. (x - 3) and (x + 5) are factors of the polynomial. (x - 3)(x + 5) = 0 (we want to know where the polynomial crosses the x-axis) So (x – 3) = 0 and (x + 5) = 0 The zeros are x = 3, x = -5

6. Practice: Find the roots of the following factored polynomials. 1.y = (x-2) 3 (x+3)(x-4) 2.y = (x-5)(x+2) 3 (x-14) 2 3.y = (x+3)(x-15) 4 4.y = x 2 (x+6)(x-6)

7. Sometimes the polynomial won’t be factored! Ex.

8. 2nd → TRACE (CALC) → 2: zero

9. Choose a point to the left of the zero. Then press ENTER. This arrow indicates that you’ve chosen a point to the left of the zero.

10. Choose a point to the rightof the zero. Then press ENTER. This arrow indicates that you’ve chosen a point to the right of the zero.

11. Press ENTER one more time!

12. Find the zeros of the following polynomials:

13. Solutions

14. End Behavior The end behavior of a graph describes the far left and the far right portions of the graph. We can determine the end behaviors of a polynomial using the leading coefficient and the degree of a polynomial.

15. First determine whether the degree of the polynomial is even or odd. Next determine whether the leading coefficient is positive or negative. degree = 2 so it is even Leading coefficient = 2 so it is positive

16. Degree EvenOdd Leading Coefficient +−+− High→HighLow→High Low→LowHigh→Low

17. Find the end behavior of the following polynomials.