Question

translation of y=|x| right 10 units and down 3 units?

Answer 1

y=|x-10|

This will shift it 10 units to the right.
To convince yourself, plug x=10 into the equation.
It gives you 0, correct?

Good that's our new vertex. It let's us know that x=10 is our new vertex.

It might seem a little unintuitive to subtract to move to the right, but hopefully that explanation helps a little bit.

We can do the same thing with the y.
To shift it down, we can apply the opposite operation to the y.

y+3=|x-10|

But we want our equation written in terms of y=stuff.
So we'll move the 3 over to the other side.

y=|x-10|-3