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What is the equation for the given table?

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-3 & 3.75 \\
\hline
-2 & 4 \\
\hline
-1 & 3.75 \\
\hline
0 & 3 \\
\hline
1 & 1.75 \\
\hline
\end{tabular}

[tex]$y = (x - 2)^2 + 4$[/tex]

Sagot :

GinnyAnsweridn
Let's find the equation of the given data set in the form [tex]\( y = a(x - b)^2 + c \)[/tex].

Given the points:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline -3 & 3.75 \\ \hline -2 & 4 \\ \hline -1 & 3.75 \\ \hline 0 & 3 \\ \hline 1 & 1.75 \\ \hline \end{array} \][/tex]

We know that the form of the equation we are looking for is:
[tex]\[ y = a(x - b)^2 + c \][/tex]

By examining the data and fitting the best curve, we find the parameters [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] that fit the data points. Through this process, we determine:

- [tex]\( a = -0.25 \)[/tex]
- [tex]\( b = -2.0 \)[/tex]
- [tex]\( c = 4.0 \)[/tex]

Thus, substituting these values into the equation, we get:
[tex]\[ y = -0.25(x + 2)^2 + 4 \][/tex]

This is the equation that represents the given data points.
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