please help me with this I need to graph y=|x-3|-2 and describe the translations. translations are when you change it, I know that but how on earth do you graph something like this? please help thank you so much!

Simplest way to understand this is to make a table of values. Pick any x to find the matching y, then plot those points

the |... anything ..|
simply means to take the positive result of 'anything'
e.g.
|5| = 5 , |-5| = 5

your graph should look like this:
http://www.wolframalpha.com/input/?i=plot+y%3D%7Cx-3%7C-2

oml you saved me thank you so much!!

To graph the equation y = |x - 3| - 2, you can follow these steps:

1. Determine the vertex: The vertex is the point where the absolute value function changes direction. In this case, the vertex is (3, -2), because when x = 3, y will be -2.

2. Plot the vertex: Mark the point (3, -2) on the graph.

3. Choose additional x-values: Pick a few x-values on each side of the vertex. You can choose values like x = 0, 1, 2, and 4.

4. Find the corresponding y-values: Plug each x-value into the equation y = |x - 3| - 2 to find the y-values.

For x = 0: y = |0 - 3| - 2 = |-3| - 2 = 3 - 2 = 1
For x = 1: y = |1 - 3| - 2 = |-2| - 2 = 2 - 2 = 0
For x = 2: y = |2 - 3| - 2 = |-1| - 2 = 1 - 2 = -1
For x = 4: y = |4 - 3| - 2 = |1| - 2 = 1 - 2 = -1

The corresponding y-values are: y = 1, 0, -1, -1.

5. Plot the points: Using the x and y-values obtained, plot the points (0, 1), (1, 0), (2, -1), and (4, -1) on the graph.

6. Connect the dots: Draw a smooth curve passing through the plotted points. Since it is an absolute value function, it will be V-shaped, opening upwards since the coefficient of x is 1.

By following these steps, you should be able to graph the equation y = |x - 3| - 2 and describe the translations. In this case, the graph is shifted 3 units to the right (positive direction) and 2 units downwards (negative direction) compared to the standard absolute value function y = |x|.