I "combined" some of the previous applets involving quadratic functions to create the applet shown above.
Browsers
Macintosh: Please use Safari
Windows: Please use Internet Explorer
Fred
In the "-1" program, this applet is meant to help with the following three outcomes:
Relations and Functions: Specific Outcomes 3
Analyze quadratic functions of the form y = a(x - p)2 + q and determine the:
Relations and Functions: Specific Outcomes 4
Analyze quadratic functions of the form y = ax2 + bx + c to identify characteristics of the corresponding graph, including:
and to solve problems.
Relations and Functions: Specific Outcomes 5
Solve problems that involve quadratic equations.
Candace
In the "-2" program, this applet is meant to help with the following two outcomes:
Relations and Functions: Specific Outcomes 1
Demonstrate an understanding of the characteristics of quadratic functions, including:
Relations and Functions: Specific Outcomes 2
Solve problems that involve quadratic equations.
Operational features (oddities?)
Standard Form
In "Standard Form" a determining location for the position of the parabola is the vertex, indicated in blue. Position the cursor over the vertex and drag to change its location (the values of "p" and "q" will update).
If you position the cursor over any other location on the parabola and drag, the "width" of the parabola will change (the value of "a" will update) and the vertex will remain at its current location.
If you move the cursor towards an x-intercept (green) or the y-intercept (red), the colored locations will fade away. This is a subtle indicator (too subtle?) that in Standard Form, dragging these locations will change the "width" of the parabola (the value of "a" will update) and the vertex will remain at its current location.
General Form
In "General Form" a determining location for the position of the parabola is the y-intercept, indicated in red. Position the cursor over the y-intercept and drag to change its location (the value of "c" will update).
If you position the cursor over any other location on the parabola and drag, one of the following will occur:
If you move the cursor towards an x-intercept (green) or the vertex (blue), the colored locations will fade away. This is a subtle indicator (again, too subtle?) that in General Form, dragging these locations will change something about the parabola such as the "width", and/or the position of the vertex (either "a" or "b" will update) and the y-intercept will remain at its current location.
Factored Form
In "Fctored Form", determining locations for the position of the parabola are the x-intercept(s), indicated in green. Position the cursor over an x-intercept and drag to change its location (the values of either "r1" or "r2" will update).
If you position the cursor over any other location on the parabola and drag, the "width" of the parabola will change (the value of "a" will update) and the x-intercept(s) will remain at their current locations.
If you move the cursor towards the vertex (blue) or the y-intercept (red), the colored locations will fade away. This is (again) an indicator that in Factored Form, dragging these locations will change the "width" of the parabola (the value of "a" will update) and the x-intercept(s) will remain at their current location.
From our meeting in June
One of the things we talked about was placing a picture in the background of the graph area, so that a student could determine the equation of a "parabolic" object, path, etc. in the picture.
The best solution would be for students to load a picture of their choosing, but in applet form the loading of a picture from a running file (not already loaded into the applet) is a security violation by the applet. As a result, this method of loading a picture is prohibited.
It is still possible for a picture of YOUR choosing, to be displayed in the graph area. An example is provided here.
Note that I could also add the feature of displaying data points of your choosing, but for now I left that feature out.
More?
If you want I could add all of the "algebra" for each piece of information displayed at the top of the applet. I had done this in a previous explorer written in C++ (which now only work on Macs running System 9). Some examples with screen shots are shown here.
Not many people used this feature, and it would take me a good month to write the code (in JAVA) to do this. If you really feel this would be worthwhile I could put it in, but the time may be better spent on other applets. Perhaps it could sit "on the shelf", and if time permits the code could be added later.
Rambling
This applet could be split into one involving "Standard Form", one involving "General Form" and one involving "Factored Form". I like all three together in one applet, but if you prefer it the other way, it can easily be arranged.
Please let me know if you would like any modifications.
The next applet I will work on is a "Linear Function" applet, similar to the "Quadratic Function" applet on this page. I know linear functions are in Grade 10, but I can build on the two applets to address two outcomes in 20-1 shown below.
Relations and Functions: Specific Outcomes 2
Graph and analyze absolute value functions (limited to linear and quadratic functions) to solve problems.
Relations and Functions: Specific Outcomes 2
Graph and analyze reciprocal functions (limited to the reciprocal of linear and quadratic functions).