Warm-Up
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![Page 1: Warm-Up](https://reader036.fdocuments.in/reader036/viewer/2022072014/56812cec550346895d91b152/html5/thumbnails/1.jpg)
Warm-Up
State an equation for the following polynomial:
-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9
x
y
![Page 2: Warm-Up](https://reader036.fdocuments.in/reader036/viewer/2022072014/56812cec550346895d91b152/html5/thumbnails/2.jpg)
Polynomial Graphing Pt. 2
![Page 3: Warm-Up](https://reader036.fdocuments.in/reader036/viewer/2022072014/56812cec550346895d91b152/html5/thumbnails/3.jpg)
Learning Targets
End Behavior
Turns or “Bumps” for each polynomial
Investigate Roots
![Page 4: Warm-Up](https://reader036.fdocuments.in/reader036/viewer/2022072014/56812cec550346895d91b152/html5/thumbnails/4.jpg)
End Behavior
Leading Coefficient Degree End Behaviors
Positive
Negative
Positive
Negative
End BehaviorDegree
Even
Even
Odd
Odd
![Page 5: Warm-Up](https://reader036.fdocuments.in/reader036/viewer/2022072014/56812cec550346895d91b152/html5/thumbnails/5.jpg)
Types of Roots
Polynomial solutions are made up of complex roots
A root is where the polynomial’s graph will intersect with the x-axis
A complex root describes two different types of roots:› Real Roots› Imaginary Roots (we will get to these next
week)
![Page 6: Warm-Up](https://reader036.fdocuments.in/reader036/viewer/2022072014/56812cec550346895d91b152/html5/thumbnails/6.jpg)
Root Classifications
We classify the type of Real Root based on the degrees of each term and how it interacts with the x-axis.
Types:› Single Root› Double Root› Triple Root› And so on…
![Page 7: Warm-Up](https://reader036.fdocuments.in/reader036/viewer/2022072014/56812cec550346895d91b152/html5/thumbnails/7.jpg)
Examples:
Single Rootsf(x)=(x-2)(x+2)
-4 -3 -2 -1 1 2 3 4
x
y
![Page 8: Warm-Up](https://reader036.fdocuments.in/reader036/viewer/2022072014/56812cec550346895d91b152/html5/thumbnails/8.jpg)
Examples:
Double Rootsf(x)=.05((x-2)^2)((x+2)^2)
-4 -3 -2 -1 1 2 3 4
x
y
![Page 9: Warm-Up](https://reader036.fdocuments.in/reader036/viewer/2022072014/56812cec550346895d91b152/html5/thumbnails/9.jpg)
Examples:
Triple Rootsf(x)=.05((x-2)^3)((x+2)^3)
-4 -3 -2 -1 1 2 3 4
x
y
![Page 10: Warm-Up](https://reader036.fdocuments.in/reader036/viewer/2022072014/56812cec550346895d91b152/html5/thumbnails/10.jpg)
You Try
Classify each type of root:
-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9
x
y
![Page 11: Warm-Up](https://reader036.fdocuments.in/reader036/viewer/2022072014/56812cec550346895d91b152/html5/thumbnails/11.jpg)
Practice
Sketch the following polynomials, describe the end behavior and classify the roots:
1)
2)
3)
![Page 12: Warm-Up](https://reader036.fdocuments.in/reader036/viewer/2022072014/56812cec550346895d91b152/html5/thumbnails/12.jpg)
#1
-19-18-17-16-15-14-13-12-11-10-9-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 9101112131415161718192021
x
y
This is only a sketch
![Page 13: Warm-Up](https://reader036.fdocuments.in/reader036/viewer/2022072014/56812cec550346895d91b152/html5/thumbnails/13.jpg)
#2
-19-18-17-16-15-14-13-12-11-10-9-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 9101112131415161718192021
x
y
This is only a sketch
![Page 14: Warm-Up](https://reader036.fdocuments.in/reader036/viewer/2022072014/56812cec550346895d91b152/html5/thumbnails/14.jpg)
#3
-18-17-16-15-14-13-12-11-10-9-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 9101112131415161718192021
x
y
This is only a sketch
![Page 15: Warm-Up](https://reader036.fdocuments.in/reader036/viewer/2022072014/56812cec550346895d91b152/html5/thumbnails/15.jpg)
Turns In a Graph
What determines the number of turns the graph of a polynomial will have?
› End Behavior› Degree of the Leading Term› Degrees of each factor, or the types of roots
The maximum number of turns a polynomial can have is (n-1) where n is the degree of the leading term
![Page 16: Warm-Up](https://reader036.fdocuments.in/reader036/viewer/2022072014/56812cec550346895d91b152/html5/thumbnails/16.jpg)
For Tonight
On the worksheet from Thursday:› Describe the end behavior using the
correct math notation
› Circle each root on the graph.› Label each root as single, double or Triple.
![Page 17: Warm-Up](https://reader036.fdocuments.in/reader036/viewer/2022072014/56812cec550346895d91b152/html5/thumbnails/17.jpg)
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