5.8, 5.9 Analyze Graphs of Polynomial Functions
Estimate the coordinates of A and B
A Represents what is known as a local maximum
B Represents what is known as a local minimum
Polynomial functions can have several turning points, which is the total number of local maximums and local minimums
• How many turning points does this function have?
• How many real zeros does is have?
• What appears to be the degree of this funciton?
Recall that the Fundamental Theorem says that the degree of a function is equal to the total number of zeros
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The degreee is given for each of the following graphs:
Determing the number of turning points for each
Degree = 3
Turning points=
Degree = 5
Turning points=
Degree = 4
Turning points=
Degree = 4
Turning points=
Degree = 3
Turning points=
Degree = 4
Turning points=
So, how is the number of turning points related to the degree?
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1. Estimatate the coordinates of all local maximums and minimums
local max:
local min:
2. Use the number of turning points to find the least degree:
3. Find the number of real zeros:
4. Use the Fundamental Theorem of Algebra to find the total number of zeros:
5. Find the number of imaginary zeros:
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Let's apply this to our Polynomania worksheet from yesterday
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Homework: pg. 390: 3-12 (on preformatted worksheet)
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