Worksheet 08-24-04
(Ray Freese)

Using a Slider Graph Applet to Explore Functions

Since our authors are discussing a library of functions, let’s use the Slider Graph Applet to help us explore this.  On your favorite browser, go to http://www.slu.edu/Classes/maymk/Applets/JCM-SLU.html and with your mouse click on Slider Graph Applet.  You should see something like the image on the bottom of this page.

In the window in the lower half of the screen you should see
a*x^2 + b*x + c  which indicates that the applet is ready to graph the function f(x)=ax^2 + bx + c for the values of a, b, c  specified at the right-hand end of the slider boxes located below the window where  a*x^2 + b*x + c appears.

With your mouse drag the square in the slider bar corresponding to “a=” until it indicates a=2. Then drag the square located in the “b=” slider box until b=-3 and finally drag the square in the “c=” box until c=-1.  You now should see the graph of f(x)=2x^2 -3x -1.

1. Is the curve concave up or concave down? ____________
2. How many of the zeros of the function are negative? ____
3. At approximately what value of x does it have a maximum or minimum value? _____
Now display the graph of f(x) = -x^2 + 4x + 1 by changing the values of a, b, c and answer the following questions:
1. Is the curve concave up or concave down? ____________
2. How many of the zeros of the function are negative? _________
3. At approximately what value of x does it have a maximum or minimum value? _________

Now consider the graphs of the family of curves ae^x+bx+c (enter the function a*exp(x) + b*x + c) and set a = 2.64, b=5 and c = -1.  Click the “Graph it!” button to display the graph of 2.64 e^x + 5x -1.
Consider the family of curves determined by keeping a=2.64, c=-1 as the parameter b varies. Answer the following questions?
1. For what value of b will the function 2.64e^x + bx - 1 have a minimum value occurring at x = 0?
2. For what value of b will the the function 2.64e^x + bx - 1 have a minimum value occurring between x= -3 and x= -1.5.  _________ 