Given, parabola having vertex is (-2, 1) and focus is (-2, 4)

As the vertex and focus share the same abscissa i.e. -2, 

parabola axis of symmetry as x = -2 

=> x + 2 = 0

Hence, the equation of aparabola is of the type

(y - k) = a(x - h)² where (h, k) is vertex

Now, focus = (h, k + 1/4a)

Since, vertex is (-2, 1) and parabola passes through vertex

So, focus = (-2, 1 + 1/4a)

Now, 1 + 1/4a = 4

=> 1/4a = 4 -1

=> 1/4a = 3

=> 4a = 1/3

=> a = /1(3 * 4)

=> a = 1/12

Now, equation of parabola is

      (y - 1) = (1/12) * (x + 2)²

=> 12(y - 1) = (x + 2)²

=> 12y - 12 = x² + 4x + 4

=> 12y = x² + 4x + 4 + 12

=> 12y = x² + 4x + 16

This is the required equation of parabola.