The Department of Mathematics and Science Education

tiffani c. knight

For this assignment, I chose to do # 2. The parabola is y=ax^2 + bx + c. I kept two of the values the same while varying the third and observed what happened. Here is the graph of the original equation :

Now, I am going to keep a and b at 2 and see graphs when c is 6, 7, 8, 9, 10, and -1.

Well, looks like when a and b are positive, the parabola opens upwards.

When a is positive and b is negative with c varying:

It also produced a parabola opening upwards.

How about when a is negative and b is positive:

Now the parabola opens downward.

Let’s try it when a is negative and b is negative:

Again, it opens downward.

This activity just confirmed what we know about parabolas: a dictates the direction of opening of the parabola: down if negative and up if positive….that makes sense.