To determine which quadratic regression equation best fits the given data points, we need to perform a quadratic regression analysis. The general form of a quadratic equation is:
[tex]\[ y = ax^2 + bx + c \][/tex]
We're looking for the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] that will result in the equation that best fits the provided data points:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-4 & 35 \\
\hline
-3 & 20 \\
\hline
-2 & 12 \\
\hline
-1 & 6 \\
\hline
0 & 2 \\
\hline
1 & 6 \\
\hline
2 & 10 \\
\hline
3 & 24 \\
\hline
4 & 38 \\
\hline
\end{array}
\][/tex]
After performing the quadratic regression analysis on these data points, the coefficients found were:
[tex]\[ a = 2.09 \][/tex]
[tex]\[ b = 0.33 \][/tex]
[tex]\[ c = 3.06 \][/tex]
Thus, the quadratic regression equation that fits the data is:
[tex]\[ y = 2.09x^2 + 0.33x + 3.06 \][/tex]
Checking the provided options, the correct answer is:
A. [tex]\( y = 2.09x^2 + 0.33x + 3.06 \)[/tex]
