QUADRATIC FUNCTIONS Investigation

By Leighton McIntyre

Goal :

Assignment 2: To show what happens to the shape and position of the graph of a quadratic function when the a is varied and the significance of the graph when a = 0.

Given the quadratic function where b = 1 and c = 2, we can choose different values of a to show what happens to the graph as a varies, THe values of a chosen are 4, 3, 2, 1, 0, -1, -2, -3, and -4. Observe what happens to the shape of the quadratic function in the diagram below:

At the a = 4 the parabola opens upwards. As the constant ** a** is varied the from 4 to -4, the graph of the function gets wider and wider then becomes flatter and flatter until it is a straight line at

This function is then tested with other values of c, like c=-1 and c = 5

In the graph to the left below, the values of ** a** range from 4 to -4, while the value of

**Summary**

1) The ** a** determines the curve of the parabola (how wide the parabola is).

2) The ** c** determines the value that the parabola cuts through the y-axis.