To find a function that models the given data, let's examine the values in the table. The table provides pairs of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] values:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & 24 \\
\hline
-1 & 17 \\
\hline
0 & 10 \\
\hline
1 & 3 \\
\hline
2 & -4 \\
\hline
\end{array}
\][/tex]
We aim to find a quadratic function of the form [tex]\( y = ax^2 + bx + c \)[/tex] that fits these data points.
After analyzing the data and fitting it to a quadratic function, we obtain the coefficients:
[tex]\[
a = -2.8353889606431945 \times 10^{-15}, \quad b = -7.000000000000002, \quad c = 10.000000000000007
\][/tex]
Thus, the quadratic function that models the data is:
[tex]\[
y = -2.8353889606431945 \times 10^{-15} x^2 - 7.000000000000002 x + 10.000000000000007
\][/tex]
To simplify, note that [tex]\( -2.8353889606431945 \times 10^{-15} \)[/tex] is very close to zero, so it doesn't significantly affect the function in a practical sense. Therefore, the quadratic function simplifies to approximately:
[tex]\[
y = -7x + 10
\][/tex]
Hence, the linear function [tex]\(y = mx + b\)[/tex] is:
[tex]\[
y = -7x + 10
\][/tex]
But strictly following the coefficients found, the exact quadratic function is:
[tex]\[
y = -2.8353889606431945 \times 10^{-15} x^2 - 7x + 10
\][/tex]
However, for practical purposes, we often use the simplified form:
[tex]\[
y = -7x + 10
\][/tex]
