Question

Type the correct answer in the box. The number of guests per month at a large resort is given in the table below, where f(x) is the number of guests, in hundreds, x months since th beginning of the year. X.0,2,4,6,8,10f(x).10,15,18,19,18,15 Use the data in the table to create the standard form of the function that models this situation, where a, b, and care constants.

Answer 1

As when x= 0, f(x)=10. We get c=10

$\begin{gathered} \begin{cases}4a+2b+10=15 \\ 16a+4b+10=18\end{cases}\rightarrow\begin{cases}-16a-8b=-20 \\ 16a+4b=8\end{cases}\rightarrow \\ -4b=-12 \\ b=3 \end{gathered}$

having that. We get

$\begin{gathered} 4a+6=5 \\ 4a=-1 \\ a=-\frac{1}{4} \end{gathered}$

so the function is

$-\frac{1}{4}x^2+3x+10=f(x)$