This can be used to "guess" a best fit quadratic polynomial for a given function. The user must input the function and the tangent line approximation at x = 0.
The graph of the function and the tangent line will appear. Now use the red box to determine a coefficient for the degree term so that the resulting quadratic approximates the curve better than the tangent line. Once that is done, you can use the green box to try to get an even better quadratic approximation.
Once you get a better approximation with the green input box, input that value in the red input box and then use the green box to get an even better quadratic approximation. This process may be repeated.