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2.8 Graph Analysis

2.8 Graph Analysis. Turning Points – the graph of a polynomial function of degree n, has at most n-1 turning points. The y-coordinate of a turning point is a local max or local min depending on which way the graph is turning Local Max Local Min.

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2.8 Graph Analysis

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  1. 2.8 Graph Analysis • Turning Points – the graph of a polynomial function of degree n, has at most n-1 turning points. • The y-coordinate of a turning point is a local max or local min depending on which way the graph is turning • Local Max Local Min

  2. Local Max and Min • Using the graphing calculator • Pg. 104 in the book

  3. Multiplicity of a Root • this is the number of times a given polynomial has a value as a root. • Assume f(x) is factored completely for each power greater than 1 the multiplicity will be greater than 1. • Ex: • Multiplicity of x=0 is 3 • Multiplicity of x=-2 is 2

  4. Exponents and Graphs • If the exponent is ODD – the graph CROSSES the x-axis at the zero with a multiplicity greater than 1 • If the exponent is EVEN – the graph TOUCHES (bounces off) the x-axis at the zero with a multiplicity greater than 1 • Ex: Graph • Using a graphing calc. • Ex:

  5. Function using graph • You can find all of the following on a graph. • Turning Points – could identify the least degree the function is. • Zeros • Local Max or Local Min

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