Quadratic fit with Wolfram Alpha

In laboratory 03 the students gather time versus distance data for a falling ball. The data from three groups was average and is presented in the table below.

time (s)	distance (cm)
0	0
0.41	100
0.47	120
0.52	140
0.56	160
0.6	180
0.64	200
0.69	220
0.73	240
0.77	260
0.83	280
0.84	300
0.9	400
0.95	500

In the laboratory the students square the time to generate a linear regression, which is then used to determine the acceleration of gravity.

The WolframAlpha computational knowledge engine provides another option to this approach. Given a set of paired data, WolframAlpha will find the quadratic least-squares fit.

To get the data into the input format expected by WolframAlpha, I used OpenOffice.org setting up a table that included the brackets and a trailing space after the comma.

{	0	,	0	},
{	0.41	,	100	},

This was copied to Notepad++ where the extraneous tabs were deleted using a find and replace, along with an extended mode find and replace using \r\n to remove the carriage returns and new line feeds. This created a string that could be pasted into WolframAlpha:

WolframAlpha then interpreted the input.

After interpretation, WolframAlpha returned the least-squares fit for the quadratic relationship along with an output chart for the residuals (not shown).