Investigating Graphs of Polynomial Functions Section 6 7

Investigating Graphs of Polynomial Functions Section 6 -7 You will use properties of end behavior to analyze, describe, and graph polynomial functions. You will identify and use maxima and minima of polynomial functions to solve problems.

Graphs of Polynomials Observations? ?

End Behavior • A description of the values of the function as x approaches positive infinity or negative infinity. • The degree and leading coefficient determine its end behavior.

Polynomial End Behavior

Example • Identify leading coefficient, degree, and end behavior.

Example • Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient.

Graphing Polynomial Functions • Step 1: Find zeros and y-intercept • Step 2: Plot zeros and y-intercept • Step 3: Make a table for several x-values that lie between zeros • Step 4: Plot points from table • Step 5: Determine end behavior • Step 6: Sketch graph

Example • Step 1: Find zeros and y-intercept • Step 2: Plot zeros and y-intercept • Step 3: Make a table for several x-values that lie between zeros • Step 4: Plot points from table • Step 5: Determine end behavior • Step 6: Sketch graph

Simultaneous Roundtable

Step 1 find zeros and yintercept Y-intercept: (0, 6) Zeros: -2, 1, and 3

Step 2 Plot zeros and yintercept

Step 3: Make a table for several x-values X Y -1 8 2 -4

Step 4 Plot points from table

Step 5: Determine end behavior

Step 6 Sketch the graph

Example

Vocabulary • Turning point – where a graph changes from increasing to decreasing or from decreasing to increasing. • Relative maximum – • Relative minimum -

Finding Maxima and Minima

Homework • Pg. 457 #2 – 14 all, 32 – 41 all, 48