The simulation at

http://phet.colorado.edu/sims/curve-fitting/curve-fitting_en.html

allows you to set points in the plane and fit linear, quadratic, cubic or quartic polynomials to those points.

To set a point you grab one from the little basket near the top right of the graph area.

Set four points more or less along a straight line, but don't make the pattern too straight.  Fit a linear, then a quadratic, then a cubic, then a quartic polynomial to the data.  Pay attention to whether the curve gets closer to the line, on the average, at each step.  Report what you see.

Now repeat with five points (you can just add a point to the ones you already have).  What happens?

Add another point and repeat.  What happens?

Now put several points along an arc and see what happens.

Give your best responses, copy them into a Submit Work Form and submit.