Add filling between a line and axis, but only in the negative region

Question

For plots like the one shown below, what is the syntax for adding filling between particular lines and the axis, but only in the negative region:

Answer 1

Here's one way:

Plot[{(x - 1)^2 - 1/2, 0}, {x, 0, 3}, PlotStyle -> {Blue, None}, 
 Filling -> {2 -> {{1}, {None, LightGray}}}]

Answer 2

Try

Plot[{Cos[x], Sin[x] + 1/2}, {x, 0, 4 Pi},  
 Filling -> {2 -> {0, {Automatic, None}}}]

Alternatively,

Plot[{Cos[x], Sin[x] + 1/2}, {x, 0, 4 Pi}, 
 Filling -> {2 -> {Axis, {Automatic, None}}}]

same picture

You can also use Filling + FillingStyle

Plot[{Cos[x], Sin[x] + 1/2}, {x, 0, 4 Pi},  
  Filling -> {2 -> 0},
  FillingStyle -> {Opacity[.3, Red], None}]

Note: For some reason, FillingStyle -> {Automatic, None} does not work.