The Department of Mathematics and Science Education

tiffani c. knight

For this assignment, I’m going to further examine the different aspects of the equation

y = ax^2 + bx + c. This time, I am going to do three things:

1. observe the graphs when a is varied from [-5, 5] and b & c stay the same.

2. observe the graph when b is varied from [-5, 5] and a & c stay the same.

3. observe the graph when c is varied from [-5, 5] and a & b stay the same.

Here we go….oh, I just kept the constant variables at 1.

When a equals -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5:

As noted in the previous assignment, and from the graph above, a determines whether the graphs open upwards or downwards; up if positive and down if negative. When a is 0, a straight line is created. Also notice that all graphs touch at the point (0, 1)

When b equals -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5:

This graph just confirmed what we know about b. b determines if the graph will shift left or right on the x axis. Here’s the part that is somewhat confusing to grasp, especially with students, but it’s just one of those things you have to remember. The graph shifts left when b is positive. The greater the number, the further left it will be. And the graph shifts right when b is negative. The more negative (meaning the smaller b gets in terms of negative numbers), the further right it goes. I say that this is confusing because we usually associate the left with negative numbers and the right with positive numbers…I guess this is a special case.

When c equals -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5:

Finally, from this graph, it appears as though c determines where the parabola will cross the y-axis.

This would be a great activity for my students to explore.