Chapter 4.3, Problem 12PPE

To determine

To find: the pattern use to complete the table. To represent the relationship using words, an equation, and a graph.

Explanation of Solution

Given information:

For the diagram below, the table gives the total number of small triangles $y$ in figure number $x$ .

  

Calculation:

Consider the following table -

$x$	$y$	$\left(x,y\right)$
1	3	$\left(1,3\right)$
2	12	$\left(2,12\right)$
3	27	$\left(3,27\right)$
4	48	$\left(4,48\right)$
5	75	$\left(5,75\right)$

Total number of small triangles is represented by $y$ and figure number is represented by $x$ . Each figure triangle contains 3 small triangles and number of large triangles is obtaining by square of figure number. Can get relative $y$ value by using equation $y=3x^2$ .

Use table to make a graph. Write independent values that are $x$ on horizontal axis and number of dependent values that are $y$ on vertical axis. Graph is as follows -