by Tim Lehman
We want to study parabolas for Assignment
#2. Parabolas are often written in the form ,
where a, b , and c are real numbers. Click
here to see the graph of the parabola of the equation
. This exercise will determine what affect
each variable has on the graph. For each section, two variables
will be fixed and the third will vary.
Fix a and b to both be 1. We will vary
the c-value in this movie from
-5 to 5.
Next, we can look at specific c-values.
For the following graph, c = -1 (black), 1 (red), 3 (purple),
5 (blue), and 7 (green).
We can see from this example that the
c -value is the y-intercept of the parabola. This is obvious when
remembering the y-intercept is when x=0.
Fix b and c to be
both 1. We will vary the value of a in this
movie from -5 to 5. Next, we will consider specifically
a equal to 4 (red), 2 (purple), 0 (blue), -2 (green), and -4 (aqua).
Again, the case when a=0 is the easiest
to visualize. This leaves y=x+1, which is the line with slope
1 and y-intercept 1. Any graph with a=0 will produce a line.
Finally, we will set a and c as 1.
In this movie, we will
vary b from -5 to 5. Again, we examine the graphs with b equal
to 4 (black), 2 (green), 0 (red), -2 (purple), and -4 (blue).
We now can see variable b adjusts the