Understand various types of patterns and functional relationships By observing similarities in the graphs of all functions of the form f(x)=ax2+bx+c, a not 0. Extend mathematical knowledge by considering the thinking and strategies of others By discussing conclusions about parameters with classmates.

Students who undertake this activity will have had prior experience which includes plotting points on a coordinate system, observing a graph pattern related to a function type (linear) and defining exponents - at least exponents included in the natural number system. Students should also be familiar with the use of some graphing tool. Students should have experience or be trained for cooperating in groups to discuss experiences and agree on a final report product.

Activities are designed to be used with a graphing utility. An introduction to the activity should include directions for the student to: Make a "good" but not necessarily point-perfect sketch of the graphs. To think about the relation between the parameters and the graph as they are working through the examples. In some way, students should be introduced to vocabulary (parabola, symmetry, parameter, y-intercept) so that communication is clear. Students should have an opportunity to discuss answers to the questions on effect of parameters with at least a partner and perhaps a small group before the large group discussion. Introduction of a symbolic method to determine axis of symmetry is optional at this point. Some general discussion of role of a and b may be sufficient at this time. (signs related to shift)

A quiz matching rules and graphs is provided. Completion of the activity, observation during discussion or student reports could also provide information on student learning.

Three groups of quadratic and linear rules to explore: on Web page

Students must have a graphing utility. Either a computer or graphing calculator will be fine. A utility where the whole rule is entered may be used or one may be available where you only need to enter a, b, c. Student printouts may be required if students have ability to paste the graphs into a document.

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