Question 732375
Here is a bit of help on your question number 2.


When you derive the equation for a general parabola through distance formula and directrix and focus, you get a result of {{{y=4p*x^2}}}, and p is the distance from the vertex to the focus and it is also the distance from the vertex to the directrix.


The shape of your parabola in #2 is the same shape as {{{y=(1/16)x^2}}}, only the position has changed.  Compare this with the general equation for the untranslated equation for a parabola.  You can get the value of p through equating 4p with (1/16).  {{{4p=(1/16)}}}.  


As for the vertex, look for the information from the given equation (which is already given in standard form) to find the "(h, k)" point.
You have {{{y=(1/16)(x-(-1))^2-2}}}, so your vertex is (-1, -2).
If you did not yet find p, do it NOW.  You are ready to find the focus [(-1, -2+p)] and the directrix.