Modeling Distance of a Fall Based on Time:
An experiment was run in a physics course to compare the distance an object falls to the time of the fall.
The data are given below.
$$
\begin{array}{l|r}
x \,\, \mbox{ sec} & y \,\, \mbox{ ft} \\ \hline
0 & 0\\
1 & 15.9\\
2 & 62.5\\
3 & 146.0\\
4 & 257.1\\
5 & 400.9\\
6 & 580.2\\
7 & 783.6\\
\end{array}
$$
a) Draw a scatter diagram for these data and determine the parabola of best fit.
(Round the coefficients of this quadratic function to three significant digits.)
b) Use this quadratic equation to estimate the distance an object would fall in 4.5 seconds.
Important Note: you will need use a graphing calculator for this POW. You will enter the data into
your calculator and it will give you the coefficients of your quadratic function.
The details for for how this is done can be found in section 8.6 of our textbook.