Mat 150 class 20
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MAT 150 – Class #20. Topics: Identify Graphs of Higher-Degree P olynomials F unctions Graph Cubic and Q uartic Functions Find Local Extrema and Absolute Extrema Modeling Cubic and Quartic Functions. Higher-Degree Polynomial Functions.

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MAT 150 – Class #20

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Mat 150 class 20

MAT 150 – Class #20

  • Topics:

  • Identify Graphs of Higher-Degree Polynomials Functions

  • Graph Cubic and Quartic Functions

  • Find Local Extrema and Absolute Extrema

  • Modeling Cubic and Quartic Functions


Higher degree polynomial functions

Higher-Degree Polynomial Functions

  • Higher-degree polynomials functions with degree ______________.

  • Examples:


Example of higher degree polynomial

Example of Higher-Degree Polynomial


Two important higher degree polynomials

Two Important Higher-Degree Polynomials

  • Cubic Function

  • Quartic Function


Key features of higher degree polynomials

Key Features of Higher-Degree Polynomials

  • In general, the graph of a polynomial function of degree n has _____________n x-intercepts.

  • Local extremaPoints - ____________on these graphs

    • Local minimum point- where the curve changes from ________________________

    • Local Maximum point – Where the curve changes from _________________________

  • Absolute Maximum Point – the ______________on the graph over an interval

  • absolute minimum point – The ______________on the graph over an interval


Graph

Graph

  • Using the appropriate window, graph .

  • Find the local maximum and local minimum, if possible.

  • Where is the absolute maximum of this function on the interval [0, 6]?


Types of polynomials

Types of Polynomials


Match the function to the graph

Match the Function to the Graph

1

2

5

3

4


Graph questions

Graph Questions

Use the given graph to graph to

  • Estimate the x-intercepts

  • Turning Points

  • Positive or negative Coefficient

  • Cubic or Quartic


Assignment

Assignment

Pg. 424-429

#1-2

#5-8 all

#11-16 all

#33-34

#41, 44, 46


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