Chapter SH, Problem 9.2.2EP

To determine

The solution of each equation by graphing.

Explanation of Solution

Given:

The given equation is:

  $n^2-8n=0$

Calculation:

Solve the given equation as:

Graph the related function $f\left(n\right)=n^2-8n$

  $\begin{array}{l}{n}^2-8n=0\\ \left(n\right)\left(n-8\right)=0\\ n=0\text{ or n - 8 = 0}\\ \text{n = 0 or n = 8}\end{array}$

The value of x-intercept is 0 and 8.

The equation of axis of symmetry is:

  $\begin{array}{l}x=-\frac{b}{2\left(a\right)}\\ =-\frac{-8}{2\left(1\right)}\\ =4\end{array}$

When x = 4, the value of f(n) = -16.

Hence, the coordinates are: $\left(4,-16\right)$ .

Taking some values of n and corresponding values of f(n) as follows:

  

The graph for these values will be: