Find the quartic function that is the best fit for the data in the table below. Report the model with three significant digits in the coefficients.
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline $\mathbf{x}$ & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\
\hline $\mathbf{y}$ & -8 & -1.25 & 0 & -1.25 & -8 & -29.25 & -80 \\
\hline
\end{tabular}
\[
y=\square
\]

Step 1 ：Given the data points, we want to find the best fit quartic function. A quartic function is of the form \(y = ax^4 + bx^3 + cx^2 + dx + e\).

Step 2 ：We use the method of least squares to find the coefficients \(a\), \(b\), \(c\), \(d\), and \(e\). This involves setting up a system of equations based on the sum of the squares of the residuals (the differences between the observed and predicted values), and then solving this system.

Step 3 ：By solving the system of equations, we find the coefficients of the quartic function to be approximately -0.250, 0, -1.000, 0, and 0. These coefficients correspond to the terms \(x^4\), \(x^3\), \(x^2\), \(x\), and the constant term, respectively.

Step 4 ：Therefore, the best fit quartic function for the given data is \(y = -0.250x^4 - 1.000x^2\).