2. Warm Up Add or Subtract the following polynomials: 1.(2x 2 – 4y + 7xy – 6y 2 ) – (-3x 2 + 5y – 4xy + y 2 ) 2.If P = 4x 4 - 3x 3 + x 2 - 5x + 11 and Q = -3x 4 + 6x 3 - 8x 2 + 4x - 3, what is P + Q?

4. Recall from Math 2 Can anyone remember what the zeros of a function are? – Where the graph touches the x-axis – The x – intercepts – Where y = 0

5. The “zero” of a function is just the value at which a function touches the x-axis. Note: This can be where it crosses or touches

6. 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

7. (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 we want to know what values of x will output 0) So (x – 3) = 0 and (x + 5) = 0 The zeros are x = 3, x = -5 NOTE: It is NOT always the opposite! What if (2x – 3) was a factor?

8. Warm Up: 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)

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

10. 2nd → TRACE (CALC) → 2: zero

11. 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.

12. 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.

13. Press ENTER one more time!

14. Find the zeros of the following polynomials:

15. Solutions

16. End Behavior The end behavior of a graph describes how the graph looks to the far left and the far right. How would you describe the end behavior of this graph?

17. End Behavior We can determine the end behaviors of a polynomial using the leading coefficient and the degree of a polynomial. Leading coefficient Degree

18. 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

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

20. Find the end behavior of the following polynomials.

21. Classwork and Homework Complete the worksheet Left Side: Class work Right side: Homework