MAT 150 – Class #20

1. 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

2. Higher-Degree Polynomial Functions • Higher-degree polynomials functions with degree ______________. • Examples:

3. Example of Higher-Degree Polynomial

4. Two Important Higher-Degree Polynomials • Cubic Function • Quartic Function

5. 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

6. 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]?

7. Types of Polynomials

8. Match the Function to the Graph 1 2 5 3 4

9. Graph Questions Use the given graph to graph to • Estimate the x-intercepts • Turning Points • Positive or negative Coefficient • Cubic or Quartic

10. Assignment Pg. 424-429 #1-2 #5-8 all #11-16 all #33-34 #41, 44, 46