Polynomial Functions and Models

Turning Points and Local Extrema

Turning point A point (x, y) on the graph Located where graph changes

from increasing to decreasing (or vice versa)

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Family of Polynomials

Constant polynomial functions f(x) = a

Linear polynomial functions f(x) = m x + b

Quadratic polynomial functions f(x) = a x2 + b x + c

Family of Polynomials

Cubic polynomial functions f(x) = a x3 + b x2 + c x + d Degree 3 polynomial

Quartic polynomial functions f(x) = a x4 + b x3 + c x2+ d x + e Degree 4 polynomial

POLYNOMIAL FUNCTIONS

GENERAL SHAPES OF POLYNOMIAL FUNCTIONS

f(x) = x4 + 4x3 – 2x – 1

QuarticFunction

Degree = 4

Max. Zeros: 4

POLYNOMIAL FUNCTIONS

GENERAL SHAPES OF POLYNOMIAL FUNCTIONS

f(x) = x5 + 4x4 – 2x3 – 4x2 + x – 1

QuinticFunction

Degree = 5

Max. Zeros: 5

POLYNOMIAL FUNCTIONS

GENERAL SHAPES OF POLYNOMIAL FUNCTIONS

f(x) = x3 + 4x2 + 2

CubicFunction

Degree = 3

Max. Zeros: 3

POLYNOMIAL FUNCTIONS

GENERAL SHAPES OF POLYNOMIAL FUNCTIONS

f(x) = x2 + 3x + 2

QuadraticFunction

Degree = 2

Max. Zeros: 2

POLYNOMIAL FUNCTIONS

GENERAL SHAPES OF POLYNOMIAL FUNCTIONS

f(x) = x + 2

LinearFunction

Degree = 1

Max. Zeros: 1

POLYNOMIAL FUNCTIONS

GENERAL SHAPES OF POLYNOMIAL FUNCTIONS

f(x) = 3

Constant Function

Degree = 0

Max. Zeros: 0