Answered

IDNLearn.com offers a unique blend of expert answers and community insights. Our experts provide prompt and accurate answers to help you make informed decisions on any topic.

Type the correct answer in the box.

The number of guests per month at a large resort is given in the table below, where [tex]$f(x)$[/tex] is the number of guests, in hundreds, [tex]$x$[/tex] months since the beginning of the year.

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline[tex]$x$[/tex] & 0 & 2 & 4 & 6 & 8 & 10 \\
\hline[tex]$f(x)$[/tex] & 10 & 15 & 18 & 19 & 18 & 15 \\
\hline
\end{tabular}

Use the data in the table to create the standard form of the function that models this situation, where [tex]$a, b$[/tex], and [tex]$c$[/tex] are constants.

[tex]$f(x) = ax^2 + bx + c$[/tex]

Sagot :

GinnyAnsweridn
Given the data points of the function [tex]\( f(x) \)[/tex], we want to find the quadratic function in standard form:
[tex]\[ f(x) = ax^2 + bx + c \][/tex]

We are given that:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|} \hline x & 0 & 2 & 4 & 6 & 8 & 10 \\ \hline f(x) & 10 & 15 & 18 & 19 & 18 & 15 \\ \hline \end{array} \][/tex]

To determine the coefficients [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex], we can use quadratic regression analysis. From this analysis, we find:

[tex]\[ a = -0.25000000000000033 \][/tex]
[tex]\[ b = 3.0000000000000036 \][/tex]
[tex]\[ c = 9.999999999999996 \][/tex]

Therefore, the quadratic function that models the number of guests per month is:
[tex]\[ f(x) = -0.25x^2 + 3x + 10 \][/tex]
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for visiting IDNLearn.com. We’re here to provide clear and concise answers, so visit us again soon.