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0.5 Graphing Polynomial Functions

 1: Introduction and Finding End Behavior of Polynomial Functions

This video covers:
*Review of what a polynomial is
*Review of the vocabulary words associated with a polynomial: Degree, Terms, Coefficients, Leading Term, Leading Coefficient, Constant Term
*How to find and use the end behavior of the graph
*What the leading term test is
*How to use the leading term test to find the end behavior of the graph
*How a even or odd degree polynomial; and how a positive or negative leading coefficient affects the end behavior of the graph
*How the steps differ between expanded form (multiplied out form) and factored form

Examples:
End Behavior Examples

 


2: Finding y-intercepts

This video covers:
*How to find the y-intercept and how it helps to graph polynomial functions
*The connection between the y-intercept and the constant term
*What format the y-intercept should be in
*How the steps differ between expanded form (multiplied out form) and factored form
*How many y-intercepts can be expected

Examples:
Y-intercept Examples

 


3: Finding the Zeros and Their Multiplicities of Polynomial Functions

This video covers:
*The definition of zero and how to find it
*How many zeros a polynomial should have
*The format the zeros should be in
*The definition of multiplicity and how to find it

Examples:
Zero and Multiplicity Examples

 


 4: Finding and Plotting x-intercepts

This video covers:
*The similarities and differences between zeros and x-intercepts
*How even and odd multiplicities affect the graph
*The format for x-intercepts
*How to plot the x-intercepts
*How the end behavior and multiplicities give a general shape to the graph

Examples:

X-intercept Examples

 


 5: Sketching Graphs of Polynomial Functions

 

This video covers:
*Putting all the steps together to graph the polynomial functions
*How the end behavior, y-intercept, zeros and x-intercepts, and multiplicities form the shape of the graph
*How many times a graph can switch directions
*How you might need to plot additional ordered pairs to fill in any missing parts of the graph

Examples:
Graphing Polynomial Examples