MAT 150 – CLASS #20 Topics: Identify Graphs of Higher-Degree Polynomials Functions Graph Cubic and Quartic Functions Find Local Extrema and Absolute Extrema.

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Presentation transcript:

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 POLYNOMIALS FUNCTIONS WITH DEGREE ______________.

EXAMPLE OF HIGHER-DEGREE POLYNOMIAL

TWO IMPORTANT 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 EXTREMA POINTS - ____________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

TYPES OF POLYNOMIALS Type of Function Degree Possible Graphs Positive Negative End Behavior Positive Leading Negative Leading Coefficient Degree Odd Or Even Linear Quadratic Cubic Quartic

MATCH THE FUNCTION TO THE GRAPH

GRAPH QUESTIONS USE THE GIVEN GRAPH TO GRAPH TO (a)ESTIMATE THE X-INTERCEPTS (b)TURNING POINTS (c)POSITIVE OR NEGATIVE COEFFICIENT (d)CUBIC OR QUARTIC

ASSIGNMENT PG #1-2 #5-8 ALL #11-16 ALL #33-34 #41, 44, 46