Question

What is the equation for the given graph expressed in the form of y=a|x-h|+k?

Answer 1

`a=5\\ \\h=0\\ \\k=-5\\ \\y=5|x|-5`

Explanation:

Consider the parent function
`y=|x|.` (The graph of this function is represented by green curve in attached diagram)

1. Stretch this function by a factor of 5. The function
`y=5|x|` represents this stretched function and the graph of this function is blue graph in attached diagram.

2. Translate the graph of the function
`y=5|x|` 5 units down and get the function
`y=5|x|-5` (red graph in attached diagram). This is exactly the graph of the function shown in the task, so

`a=5\\ \\h=0\\ \\k=-5`