Chapter 9.6, Problem 17E

To determine

Describe and correct the error in finding the amplitude.

Answer to Problem 17E

  $\boxed{\left|a\right|=8}$

Explanation of Solution

Given information:

Maximum point $=\left(2,10\right)$

Minimum point $=\left(4,-6\right)$

  $\begin{array}{l}\left|a\right|=\frac{\left(\text{maximum value}\right)+\left(\text{minimum value}\right)}{2}\\ =\frac{10-6}{2}\\ =2\end{array}$

Formula used:

Amplitude $=\left|a\right|=\frac{\left(\text{maximum value}\right)-\left(\text{minimum value}\right)}{2}$

In the given information we are having amplitude formula as

  $\left|a\right|=\frac{\left(\text{maximum value}\right)+\left(\text{minimum value}\right)}{2}$ but the correct formula of amplitude is

  $\left|a\right|=\frac{\left(\text{maximum value}\right)-\left(\text{minimum value}\right)}{2}$ .

Now finding the value of amplitude using formula:

  $\begin{array}{l}\left|a\right|=\frac{\left(\text{maximum value}\right)-\left(\text{minimum value}\right)}{2}\\ \left|a\right|=\frac{10-\left(-6\right)}{2}=\frac{10+6}{2}\\ \left|a\right|=\frac{16}{2}\\ \boxed{\left|a\right|=8}\end{array}$