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Page 1: Section 2.3: Polynomial Functions of Higher Degree with Modeling April 6, 2015

Section 2.3:Polynomial Functions of

Higher Degree with ModelingApril 6, 2015

Page 2: Section 2.3: Polynomial Functions of Higher Degree with Modeling April 6, 2015

General Shape of Polynomial Functions

Page 3: Section 2.3: Polynomial Functions of Higher Degree with Modeling April 6, 2015

Standard vs. Factored Form

1 21 2 3 ...n n ny a x a x a x

1 2 3( )( )( )...y x z x z x z

•General Shape•Y-intercept

•General Shape•X-intercept(s)

Page 4: Section 2.3: Polynomial Functions of Higher Degree with Modeling April 6, 2015

Multiplicities of Zeros

Multiplicity of 1

Multiplicity of 2

Multiplicity of 3

Page 5: Section 2.3: Polynomial Functions of Higher Degree with Modeling April 6, 2015

Identifying Degrees and Zeros

2 3( 3) ( 5)y x x 2( 2)( 4)y x x x

2 11 28y x x 3 210 13 24y x x x

Page 6: Section 2.3: Polynomial Functions of Higher Degree with Modeling April 6, 2015

Solve.

3 212 9 22 0x x x

Page 7: Section 2.3: Polynomial Functions of Higher Degree with Modeling April 6, 2015

Given the zeros, write an equation for each polynomial in standard form.

Zeros: -6, 1, 9

Zeros: 7, 7,3

Page 8: Section 2.3: Polynomial Functions of Higher Degree with Modeling April 6, 2015

Mix-and-Match Activity

If you were given a card with zeros, write the equation for the polynomial in standard form.

If you were given a card with an equation of a polynomial, determine the zeros of the function.

NOW, find the person that you match up with.


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