Please help i've been on this forever

as the vertex  (−2,5)  and focus  (−2,6)  share same abscissa i.e.  −2, parabola has axis of symmetry as  x=−2  or  x+2=0

hence, equation of parabola is of the type  (y−k)=a(x−h)2, where  (h,k)  is vertex. its focus then is  (h,k+14a)

as vertex is given to be  (−2,5), the equation of parabola is

y−5=a(x+2)2

and its focus is  (−2,5+14a)

therefore  5+14a=6  or  14a=1  i.e.  a=14

and equation of parabola is  y−5=14(x+2)2

or  4y−20=(x+2)2=x2+4x+4

or  4y=x2+4x+24