Chapter 3.8, Problem 26PPS

To determine

To graph the function $f(x)=-\frac{147}{115}\left|x-115\right|+147$ and determine the height of the Great Pyramid when it was originally built.

Answer to Problem 26PPS

147 m

Explanation of Solution

Given:

Function: $f(x)=-\frac{147}{115}\left|x-115\right|+147$

Concept used:

The general form of an absolute value function is $f(x)=a\left|x-h\right|+k$ .

The graph of $f(x)=a\left|x-h\right|+k$ is a “V” with vertex $\left(h,k\right)$ , slope $m=a$ on the right side of the vertex $\left(x>h\right)$ and slope $m=-a$ on the left side of the vertex $\left(x<h\right)$ .

The graph of $f(x)=-a\left|x-h\right|+k$ is an upside-down “V” with vertex $\left(h,k\right)$ , slope $m=-a$ for $\left(x>h\right)$ and slope $m=a$ for $\left(x<h\right)$ .

Calculation for graph:

Consider $f(x)=-\frac{147}{115}\left|x-115\right|+147$

Compare with the general form:

  $g(x)=a\left|x-h\right|+k$

Here, the value of $a=-\frac{147}{115}$ , so the graph opens downwards with a slope of $-\frac{147}{115}$ .

The value of $h=115$ and the value of $k=147$ , so the vertex of the graph is $\left(115,147\right)$ .

Values of x	Values of g (x)
0	$0$
1	$\frac{147}{115}$
2	$\frac{294}{115}$

By taking different values of x , the graph can be plotted.

Graph:

The graph of $f(x)=-\frac{147}{115}\left|x-115\right|+147$ :

  

Interpretation:

Since $f(x)$ is the height function of the pyramid, when the pyramid was originally built, the height of the pyramid was 147 m.

Conclusion:

Therefore, the height of the pyramid, when it was originally built, was 147 m.