1. Homework Check

2. End Behavior, Extrema & Sketching

3. Look left and right, to figure out what’s happening up and down.
End Behavior
Look left and right, to figure out what’s happening up and down.
right
up or down
up or down
leftt

4. End Behavior: From a Graph1. 2. 2.

5. End Behavior: From a Graph3. 3. 4.

6. 5. f(x) = x4 + 2x2 – 3x 6. f(x) = -x5 +3x4 – x 7. f(x) = 2x3 – 3x2 + 5
Determine the left and right behavior based on the equation.
5. f(x) = x4 + 2x2 – 3x
6. f(x) = -x5 +3x4 – x
7. f(x) = 2x3 – 3x2 + 5

7. Tell me what you know about the equation…
Odd degree
Positive leading coefficient

8. Tell me what you know about the equation…
Page 261 #53
Even degree
Negative leading coefficient

9. Tell me what you know about the equation…
Page 261 #54
Odd degree
Positive leading coefficient

10. Extrema are turns in the graph.
If you are given a graph take the turns and add 1 to get the least possible degree of the polynomial.
If you are given the function, take the degree and subtract 1 to get the extrema.
f(x) = 2x3 – 3x2 + 5
3rd degree, 2 extrema
4th degree, 3 extrema

11. 8. What is the least possible degree of this function?

12. 9. What is the least possible degree of this function?

13. What if you didn’t have a graph?
10. f(x) = x4 + 2x2 – 3x
Number of Extrema: ____
11. f(x) = -x5 +3x4 – x
Number of Extrema: ____
12. f(x) = 2x3 – 3x2 + 5
Number of Extrema: ____

14. Sketching:
# of Zeros: _________ Y-Int: ________ 1

15. Sketching:
# of Zeros: _________ Y-Int: ________

16. Homework:
Worksheet
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