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The annual enrollment of a university for the last nine years is recorded in the table below.

\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|}
\hline
Year & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
\hline
Students (thousands) & 9.5 & 8 & 8.5 & 7.5 & 6.5 & 6.5 & 8.5 & 8.5 & 9 \\
\hline
\end{tabular}

What quadratic function best models this set of data?

[tex]\[ y = \square x^2 + \square x + \square \][/tex]

Sagot :

GinnyAnswer
To determine the quadratic function that best models the given set of data, we need to identify the coefficients [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] of the quadratic equation in the form [tex]\( y = ax^2 + bx + c \)[/tex].

After analyzing the provided data and performing polynomial regression, the coefficients are found as follows:
- [tex]\( a = 0.14015151515151508 \)[/tex]
- [tex]\( b = -1.4265151515151515 \)[/tex]
- [tex]\( c = 10.75 \)[/tex]

Thus, the quadratic function that models the given set of data is:

[tex]\[ y = 0.14015151515151508 x^2 - 1.4265151515151515 x + 10.75 \][/tex]
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