From: Mary Lou (for Teacher2Teacher Service)
Date: Apr 13, 1998 at 21:52:18
Subject: Re: TI-82 graphing calculator and parabolas

What is interesting for students to find out is what the effect of a change in 
a, b, or c will have on the graph of a parabola. 

Start with a given equation where a, b and c are known. Have students draw several 
parabolas by keeping a and b as given, and change c. They should see that for some 
values of c there are no roots, one root, or two roots. They should also notice 
that the shape of the parabola stays the same (congruent) and that the y-intercept 
and vertex changes. For those equations that have roots, they can be found by
using the CALC menu.

Similarly, keep b and c as given and change the values of a for a both positive 
and negative, as well as larger than one and between zero and one. Students should 
see that the vertex does not remain the same, the y-intercept changes, and that 
the number of roots as well as the value of roots changes.

Similarly, keep a and c as given and change the values of b. When the values of b 
change in sequence, the movement of the parabola's vertex is the path of another 
parabola. The vertex changes, the y-intercept remains the same but the number and 
value of the roots change.

You mentioned that you had a TI-82. I am using a TI-83. The 82 may have the same 
feature. Try it. In your y= menu enter an equation:

   y = 2x^2 - 5x + { -3, -2, -1, 0, 1, 2, 3 } 

The seven graphs will be drawn in sequence. This is where I believe that the 
graphing calculator is so meaningful for instruction. Similarly, replace the
value of 2 with a set of numbers such as 

   { -4, -2, -1, -0.5, 0, 0.25, 0.5, 1, 2, 4 } 

and keep one of the c values. The motion of the graphs is great!

Hope that this gives you some ideas.

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