ANSWER
[tex]y = - 1+ 2 \sin(2x - 1)[/tex]
EXPLANATION
The given equation is
[tex]y = 1 + 2 \sin(2x - 1)[/tex]
This function is of the form,
[tex]y = a \sin(bx - c) + d[/tex]
The value of d=1 shifts the graph up by one unit.
If we want to shift the graph, 2 units down, then, we have to add -2 to d=1.
The transformed equation is,
[tex]y = - 2 + 1 + 2 \sin(2x - 1)[/tex]
which gives us,
[tex]y = - 1+ 2 \sin(2x - 1)[/tex]
