This learning activity allows the student to explore how the parameters of a quadratic relate to its graph. It also compares the quadratic in standard form with the quadratic in general form.
Type of Material:
Classroom demo; student exploration
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Identify Major Learning Goals:
The successful student will learn about the relationship between a quadratic function and the graph.
Target Student Population:
Intermediate algebra and Precalculus students
Prerequisite Knowledge or Skills:
The activities assume no prior knowledge other than the Cartesian coordinate system.
This learning object consists of a graphing tool accompanied by four activities. On the left is a frame containing well written instructions that guide the student through the activities. The frames width can easily be resized. On the right is the graphing tool. In the activities, the student is asked to enter the graph of y = a*x^2+b*x+c and is instructed to change the parameters a, b, and c to explore the effect on the graph. The parameters can be inputted, incremented manually, or automatically so that the student can explore the effect on the graph when the parameters change. Instead of telling the student what to do, the activities ask to students to explore on their own. The concepts become more advanced as the student uses completing the square to investigate the relationship between the parameters and the graphs.
Reformatting the left activity frame to use bulleting, numbering, or some other organizational technique would make the instructions easier to follow.
Potential Effectiveness as a Teaching Tool
The object can be used by students learning on their own without the assistance of an instructor. The student using this activity will have the opportunity to explore the graphs of quadratics without getting frustrated. Completion of this activity requires the student to manipulate formulas on paper and experiment extensively with the results to investigate the more advanced concepts of quadratic functions and their graphs.
The variable w has multiple uses in the applet; this can be confusing to the user. The w is used as a view dimension, and in the activity directions to Plot (x-v)*(x-w). The animation controls also use a double v,
which appears on the screen as a w.
The animation can be extremely quick, depending on the users computer. An additional comment that using a value of E that is negative will produce a slower graph would be helpful to the student who does not realize this in advance.
The text does not provide a summary of the concepts so that the user is unable to benchmark his/her own conclusion with the concept being investigated.
Ease of Use for Both Students and Faculty
The instructions for each of the activities are easy to follow. If the student follows the directions then there should be no difficulties in using this learning object. A help link that gives explanations on how to use the graphing tool is provided.
It is very difficult to distinguish two equations that have the same graph using different colors for the graph. The applet does not toggle between the two colors, leaving the user to wonder if the second graph is on the screen. Instead the applet assigns one color to both equations, regardless of the instructions given by the user. To observe the second color, the user must delete the function that controlled the first color.
The requirement of using * to indicate multiplication is cumbersome since most graphing utilities now use syntax with implied multiplication. The parameter controls for animation could be enlarged and separated so that they do not overlap. It would be helpful to have the Stop button also present for the expanded animation controls.
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