polynomial functions unit 4. polynomials monomial—a number, variable, or product of numbers and...
TRANSCRIPT
Polynomials
• Monomial—a number, variable, or product of numbers and variables all raised to whole number powers
• Polynomial Expression--a monomial or sum of monomials.
• Polynomial Function—function that is defined by a polynomial expression
• Leading coefficient—coefficient of highest powered term
• Degree of polynomial—power of highest powered variable
Standard Form
The standard form of a polynomial function arranges the terms by degree in descending numerical order
A polynomial function P(x) in standard form is:
Where n is a nonnegative integer and are real numbers. Ex:
Classifying Polynomials by degree• d=0 Constant
• d=1 Linear
• d=2 Quadratic
• d=3 Cubic
• d=4 Quartic
• d=5 Quintic xxx
xxxx
x
xx
x
23
2289
64
12
2
52
45
234
3
2
Classifying by Number of Terms
• Monomial—one term
• Binomial—two terms
• Trinomial—three terms
• N-nomial—n terms
Graphs of Polynomial Functions
• Constant Linear Quadratic• Show graphs with positive and negative LC
Graphs of Polynomial Functions
• Quadratic: D:________R: ________Zeros: _______Inc: _______Dec: _______as as
Graphs of Polynomial Functions
• Cubic: D:________R: ________Zeros: _______Inc: _______Dec: _______as as
Graphs of Polynomial Functions
• Quartic: D:________R: ________Zeros: _______Inc: _______Dec: _______as as
Graphs of Polynomial Functions
• Quintic: D:________R: ________Zeros: _______Inc: _______Dec: _______as as
To sketch the graph
• Determine the end behavior.
• Determine the x intercepts (where y=0)
20
020
)2(0
20
2)(2
2
xandx
xandx
xx
xx
xxxf