Chapter 4, Problem 63SGR

To determine

To find: The function of the model.

Answer to Problem 63SGR

The function of the model is $\left(5,25\right)$ .

Explanation of Solution

Given information:

The given model is.

  

Calculation:

A product of $2$ number with a sum of $10$ gives a function that model download direction as follows.

  $y=-x^2+10x$

Complete square method.

  $\begin{array}{c}\left(\frac{10}{2}\right)={\left(5^{}\right)}^2\\ =25\end{array}$

Add and subtract $25$ the equation as follows.

  $\begin{array}{l}y=-x^2+10x+25-25\\ y=-{\left(x-5\right)}^2+25\\ y=a{\left(x-h\right)}^2+k\end{array}$

Compare the above to equation then.

  $\begin{array}{l}a=-1,h=5,k=25\\ \end{array}$

The vertex $\left(h,k\right)=\left(5,25\right)$

The axis of symmetry $x=5$

Thus, the number $\left(5,25\right)$ gives a maximum product.

Therefore, the function of the model is $\left(5,25\right)$ .