Is purchasing an extended warranty on a vehicle a good investment that
favors me as a consumer?

The company that sells a warranty is in business to make money.
Therefore, they are betting they will pay out less (much less) in
warranty payments than they will bring in from sales.

This means a purchased warranty is a suckers bet... UNLESS something
unknown to anyone will occur.

But how do you predict that?

Hence the term insurance.  Its always a risk-management tool.  I would
read the extended warranty and ask the sales guy to go to the car and
point out what is not included.  I would proceed to write those down,
as you would be surprised.  Also, ask for specifics.  When he says
that the body will be assured against rust, ask about the little
lining around the window.  You would be surprised.  When he says
bumper to bumper, ask about mufflers, radiators, bushings, etc.  If he
doesn't give you any exceptions, then he's either not fully aware or
not telling the whole truth.  I may be wrong, but most extended
warranties don't cover everything.

Long story short, is after you get this honest feedback, ponder on if
the extended warranty is worth it.  Most times it is not.  However, it
may increase the resale value of the car.