Answer:
There is a horizontal tangent at (0,-4)
The tangent is vertical at (-2,-3) and (2,-3).
Step-by-step explanation:
The given function is defined parametrically by the equations:

and

The tangent function is given by:


The tangent is vertical at when 





When t=1,
and 
When t=-1,
and 
The tangent is vertical at (-2,-3) and (2,-3).
The tangent is horizontal, when
or 


When t=0,
and 
There is a horizontal tangent at (0,-4)