Consider the given function and the table. Now, with the help of the values given in the table, plot a graph as, Here, it can be seen that by plotting the data, the obtained graph represents a parabola. Therefore, the function which represents the data table is \(\displaystyle{g{{\left({x}\right)}}}={c}{x}^{{{2}}}\). The point \(\displaystyle{\left(-{4},\ -{32}\right)}\) is on the graph. So, substitute the point, \(\displaystyle{\left(-{4},\ -{32}\right)}\), in \(\displaystyle{g{{\left({x}\right)}}}={c}{x}^{{{2}}}\).

\(\displaystyle-{32}={c}{\left(-{4}\right)}^{{{2}}}\)

\(\displaystyle-{32}={c}{\left({16}\right)}\)

\(\displaystyle{\frac{{-{32}}}{{{16}}}}={c}\) Solving further, \(\displaystyle{c}=\ -{2}\) So, \(\displaystyle{g{{\left({x}\right)}}}=\ -{2}{x}^{{{2}}}\) Hence, the function that can be used to model the data is \(\displaystyle{g{{\left({x}\right)}}}={c}{x}^{{{2}}}\) and the value of constant is \(\displaystyle{c}=\ -{2}\).