Answered

Look at this table:
\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-6 & -216 \\
\hline
-5 & -150 \\
\hline
-4 & -96 \\
\hline
-3 & -54 \\
\hline
-2 & -24 \\
\hline
\end{tabular}

Write a linear [tex]\((y = mx + b)\)[/tex], quadratic [tex]\(\left(y = ax^2\right)\)[/tex], or exponential [tex]\(\left(y = a(b)^x\right)\)[/tex] function that models the data.

[tex]\[ y = \][/tex]
[tex]\[ \square \][/tex]



Answer :

GinnyAnswer
To determine the equation that best models the given data, we can analyze the points provided in the table:

[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -6 & -216 \\ \hline -5 & -150 \\ \hline -4 & -96 \\ \hline -3 & -54 \\ \hline -2 & -24 \\ \hline \end{array} \][/tex]

We need to decide whether a linear, quadratic, or exponential function best fits the provided values. Let us focus on finding a quadratic function of the form [tex]\(y = ax^2 + bx + c\)[/tex].

From thorough analysis, we determine the quadratic best fitting function for the data. The quadratic equation found is of the form [tex]\(y = ax^2 + bx + c\)[/tex] where:
- [tex]\(a = -6\)[/tex]
- [tex]\(b = 0\)[/tex]
- [tex]\(c = 0\)[/tex]

Substituting these values into the quadratic equation, we have:

[tex]\[ y = -6x^2 \][/tex]

Therefore, the model that best fits the given data is:

[tex]\[ y = -6x^2 \][/tex]