1. Below you will find an applet for the least squares best fit to a quadratic equation given by

h = ax² + bx + c.

Since there are only three data points, the best quadratic always fits the data exactly.

a. Enter the data set number 1 in the upper right corner of the applet to get your first data set. Adjust the parameters for the coefficients a, b, and c until you find a sum of squares value of 0.0. (Hint: The coefficients are integer valued.) Write the equation for this quadratic, then determine the values of the x and h-intercepts and the coordinates of the vertex.

b. Repeat the process in Part a. for the data set number 2 in the upper right corner of the applet.

c. Write a brief discussion on what you observe as you increase c. Similarly, write a brief description of what happens to the graph of the quadratic as you change b and a. Be sure to describe what happens as a changes sign. You may find that the changes caused by varying b are different when a is less than zero. In your discussion, you should clearly write about each case of the parameters, a, b, and c, as they vary, noting differences when the parabola changes from pointing up to pointing down. For each case, describe what happens to the vertex (direction of shifts), the distance across the parabola, and/or the direction of opening of the parabola.