This task guides students to discover the relationships between the degree and leading coefficient of a polynomial function and specific characteristics of the graph such as the domain, range, end behaviors, turning points, and extrema. Students analyze the graphs of 13 different polynomial functions to draw conclusions about these relationships.
This file includes:
-13 polynomial functions written both standard & factored form, along with their graphs
-A chart for students to record the characteristics of the 13 graphs
-Analysis questions to guide students in drawing their conclusions
-A practice set to gauge student understanding of the patterns discovered in this activity
-Answer keys to all parts of the activity
This activity was designed for use in an Honors Algebra 2 class, but can be used in an on-level Algebra 2 class as well. Suggestions for modifications that will make this successful in varying levels of classes are provided in the Teaching Tips.
This activity takes 2 to 3 50 minute class periods depending on the level of the students. While this is longer than it would take to teach the same patterns via direct instruction, I have found that students gain a deeper understanding of the relationships between the characteristics and they retain their knowledge much longer by discovering these patterns for themselves.