Polynomial Review
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Transcript of Polynomial Review
Polynomial Review
OBJ: SWBAT analyze and graph polynomials
Definition
Definition: A polynomial function is a function where….
Terms:
Analyzing Standard Form
F(x) = Key Info:Degree:Leading Coefficient:Y-intercept:# roots:# extrema:
Analyzing Standard Form Con’t.d
End Behavior
Positive Negative
Even
Odd
Example
f(x) = 7x5 – 2x2 + 9Deg: ____LC: ____Y-int: ____E.B.: ____# roots: ____# extrema: ____
Factored Form
F(x) = a(x – f1)n(x – f2)n…..
Where….
Degree:LC:Y-int:**
Example:
f(x) = -2(x – 3)2(x + 4)4(2x – 1)2
Deg: ____LC: ____Y-int: ____E.B.: ____# roots: ____# extrema: ____Roots: ____
X-intercepts
X-intercepts = roots = zeroes If k is a root, then f(k) = 0 or (x – k) is
a factor How to determine:
Synthetic or Long Division
Synthetic Division Example
Divide 3x3 – 2x2 + 6 by x + 1
Tips to Finding Roots
1) Descartes Theorem:
2) Rational Roots Theorem
3) Use division to verify
Example
f(x) = x3 – x2 – 25x + 25
Steps to Graphing
1)2)3)4)5)
Example
f(x) = x4 – x3 – 21x2 + x + 20