Section 2.3:Polynomial Functions of
Higher Degree with ModelingApril 6, 2015
General Shape of Polynomial Functions
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)
Multiplicities of Zeros
Multiplicity of 1
Multiplicity of 2
Multiplicity of 3
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
Solve.
3 212 9 22 0x x x
Given the zeros, write an equation for each polynomial in standard form.
Zeros: -6, 1, 9
Zeros: 7, 7,3
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.