Exploring the graphs of the palabola


Problem 1

1. Construct graphs for the parabola

for different values of a, b, and c. (a, b, c can be any rational numbers).

I have graphed the parabola as follows : First of all, let's fix the a=b=1, and take the different values of c=1, 2, 3, 4, 5. In the second window of the graphs, I fix the a=c=1 and take b=1, 2, 3, 4, 5. The last case shows the graphs of b=c=1 and a=1, 2, 3, 4, 5.

The fist case, the graphs are moving upward on the y-axis while second and third cases has the fixed point of the movement. After that, I added the animation of the second and third cases together in the same window. The red parabola shows the second case, and the blue parabola shows the third case. I used the variable n from -10 to 10 in both cases.

To see the animaition, click here.