My son (in Algebra 2) has been given an assignment asking him to tell
whether several different equations show exponential growth or decay,
and to JUSTIFY. Some examples are:
2(-0.33x)^2
and
3((0.75)^-2)x
Can somebody explain how to figure out (at the 9th grade level)
whether a certain equation shows growth or decay? And since you can't
use a calculator, I cannot simply graph it to justify my answer.

Plug in different values for x.  

If when X increases the solution increases, then you have growth.  
If when X increases the solution decreases, then you have decay.

Er.. Jack, do you not mean the implicit Y ?

Sure, you can call it an implicit Y.  However I'd just assume to
ignore the need to have an equals sign and a variable on the other
side of the equation... and simply simplify what you have.

Kinda like...
What is 2 X 4
or
392Y + 219Y

In either case, any reasonable math person knows they can simplify
things without the need of an equals sign.