by Tim Lehman

Assignment #2

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 graph horizontally.