5.2/5.9 Polynomial & Linear Factors

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Presentation transcript:

5.2/5.9 Polynomial & Linear Factors Learning goals graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior

The following are equivalent statements about a real number b and a polynomial P(x): (x – b) is a factor of P(x) b is a zero of the function b is a root (or solution) of P(x) = 0 b is an x-intercept of the graph

So, for example… Equivalent Statements about Polynomials – 4 is a solution of – 4 is an x-intercept of the graph – 4 is a zero of (x + 4) is a factor of

Ex 1 Find the zeros, graph, find relative max/min.

Ex 2 Find the zeros, graph, find relative max/min

Ex 3 Write an equation in standard form with zeros at

Vocabulary multiple zero : a repeated zero of a polynomial that occurs because of a repeated linear factor multiplicity : the number of times a zero occurs in a polynomial

Ex 4 For the following polynomial, find any multiple zeros and state the multiplicity of each

Transformation Types Review reflection horizontal shift vertical shift stretch/compression Power Function

Ex 5 What is the equation of the following function that has been translated down 1 unit, left 6 units, and vertically stretched by a factor of 3 ?

Ex 6 What is the equation of the following function that has been reflected over the x- axis, translated up 2 units, right 3 units, and vertically compressed by a factor of ½ ?