91Ó°ÊÓ

A small manufacturing firm collected the following data on advertising expenditures A (in thousands of dollars) and total revenue R (in thousands of dollars).

The scatter plot of the given data is

From the given function it is clear that $a<0$, this indicates that the parabola opens down. The function has a maximum at the vertex of the parabola. The optimal level of advertising is A for which the function reaches its maximum value,

$$\begin{gathered} A=-\frac{b}{2a} \\ A=-\frac{411.88}{2·\left(-7.76\right)} \\ A≈26.5 \end{gathered}$$

The optimal level of advertising is spent when,$A=26.5$,

Substitute $R\left(26.5\right)$in the given function $R\left(A\right)=-7.76A^2+411.88A+942.72$

So the total revenue is

$R\left(26.5\right)=6408.08$

Plot the given coordinates on a cartesian coordinate plane and in the same plane, and plug in the equation to see if the equation is the best fit.

The graph of the function together with the coordinate of the data is

All the points seem to be located along with the graph of the $y=-7.76A^2+411.88A+942.72$

Therefore the given function is the best fit function.

Using the information from the table and the given function $R\left(A\right)=-7.76A^2+411.88A+942.72$

The graph of the quadratic function of best fit on the scatter diagram is