Question 750606
The focal length is {{{abs(3-(-2))=5}}}.  You should reread the book discussion about deriving the equation for a parabola.  if p is the focal length, then a standard position parabola is {{{4py=x^2}}}, or {{{y=(1/(4p))x^2}}}.


You should use the standard form for a parabola, since you know your vertex, as given (-4,3).  Putting this information into the standard form equation, you have {{{y=(1/(4p))(x+4)^2+3}}}
and because you know p=5, the focal length,
{{{y=(1/(4*5))(x+4)^2+3}}}
{{{highlight(y=(1/20)(x+4)^2+3)}}}


You can leave in standard form, or you can multiply and simplify the right hand side into general form.  




*____Note that the standard form equation for a parabola is {{{y=a(x-h)^2+k}}}  where the vertex is (h,k).