Answer:
y = -|x -3| +2
Explanation:
You want the values of the horizontal and vertical translation of the absolute value function.
Transformation
When a function g(x) undergoes a transformation that includes ...
- vertical scaling by a factor of 'a'
- horizontal translation 'h' units to the right
- vertical translation 'k' units up
the transformed version of the function will look like ...
y = a·g(x -h) +k
Absolute value function
When g(x) = |x|, these transformations make it look like ...
y = a·|x -h| +k
Application
Your function has a = -1, which causes the graph to be reflected over the x-axis. In the attachment, the original function y=|x| is shown in green. The version y=-|x| is shown in red, reflected over the x-axis.
The version shown in blue matches your graph. It is the reflected function with its vertex moved from (0, 0) the (3, 2). That is, (h, k) = (3, 2).
These values go into the boxes in your answer form:
y = -|x -3| +2