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.
Answer the following questions:
Is the curve concave up or concave down? ____________
How many of the zeros
of the function are negative? ____
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:
Is the curve concave up
or concave down? ____________
How many of the zeros
of the function are negative? _________
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?
For what value of b will
the function 2.64e^x + bx - 1 have a minimum value occurring at x = 0?
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. _________
