A quadratic function f(x) = ax^2 + bx + c is specified by the three constants a, b, and c, which we will refer to as parameters.

By completing the square (a process we will learn on Monday), we can express this same function by f(x) = a(x-h)2 + k so that the quadratic function f(x) is equally well specified by the three parameters a, h, k.

It is easier to understand how a,h, k are related to the parabola that is the graph of f(x). So, we will use the applet (found at http://members.shaw.ca/ron.blond/QFA.CSF.APPLET/ ) to draw the graph of f(x) = a(x-h)2 + k. Click on the website or copy it into your browser and you will see an interactive applet that looks like this:

At the website, you can select values for a,h,and k (between -9 and 9) by moving the sliders in order to see how the graph changes. You can also move the graph itself and note how the values a,h,and k change. Further directions for using the slider applet are located on the same page directly below the applet.

Investigation: Describe the effect of changing each of a, h, and k on the shape or position of the parabola. Be as specific as you can.

Please bring to class, on Wednesday, your description of this investigation... you may make a list of observations, write in paragraph form, whatever works best for you in terms of organizing your findings.