# 6.2 KEY - repeated zeros 2 3 4 8 6 x x x x f = 9 3 3-= x x...

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1 Section 6.2 Zeros of polynomial functions Obejctives s Find the zeros (and their multiplicity) of a polynomial function s Understand the relationship between zeros, roots, solutions, x -intercepts and factors of a polynomial What is the difference between a polynomial and a polynomial function? 12 2 + - x x 12 ) ( 2 + - = x x x f s Let’s talk about graphs of polynomial functions 1 linear 4 quartic 3 cubic 2 quadratic Example function Example graph Degree Find the zeros and graph ) 3 )( 1 )( 2 ( + + - = x x x y ) 3 )( 1 ( ) ( 2 + + = x x x x f In this case, the root 0 happens twice. What do you notice about the graph at this root? Multipliciy s A repeated zero has a multiplicity equal to the number of times the zero occurs. s The multiplicity of a zero affect the graphs behavior at that value.

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2 Find all the zeros of the function, then state the multiplicity of any
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Unformatted text preview: repeated zeros 2 3 4 8 6 ) ( x x x x f + + = ) 9 ( ) 3 ( 3 +-= x x y Write a polynomial s Write a polynomial function in standard form with zeros -2, 3, and 3. s HINT: Use the Zero Product Property in reverse. Write a polynomial function in standard form with zeros 0, 1, and -3. Summary! s The following 4 statements are equivalent s-4 is a solution of s-4 is an x-intercept of the graph of s-4 is a zero of s X + 4 is a factor of 4 3 2 =-+ x x 4 3 2-+ = x x y 4 3 2-+ = x x y 4 3 2-+ x x Summary Questions s-3 is a zero of s Tell me one of the factors of s True / False 3 is an x-intercept of the graph of 6 2-+ = x x y 4 3 2-+ x x 6 2-+ = x x y Assignment # ___ s Page 311 (17-31 odd) &amp;amp; 35...
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## This note was uploaded on 05/13/2011 for the course MTH 98 taught by Professor Johnson during the Fall '09 term at Grand Valley State.

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6.2 KEY - repeated zeros 2 3 4 8 6 x x x x f = 9 3 3-= x x...

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