Question 609826
  <pre><font face = "Tohoma Ital" size = 3 color = "indigo"><b> 
Hi
Note: the vertex form of a parabola opening up or down, {{{y=a(x-h)^2 +k}}} where(h,k) is the vertex.
y-2+-1/8(x+2)^2   ||Assuming you meant: y - 2 = (-1/8)(x+2)^2
y = (-1/8)(x+2)^2 + 2   ||Vertex(-2,2), axis of symmetry is x = -2
The standard form is {{{(x -h)^2 = 4p(y -k)}}}, where  the focus is (h,k + p)
  (x+2)^2 = -8(y-2)^2 , 4p = -8, {{{p = -2}}}  and focus is (-2,0), directrix is y= 4
{{{drawing(300,300,-10,10,-10,10,  grid(1),blue(line(-2,10,-2,-10)),   
circle(-2, 2,0.3),
circle(-2, 0,0.3),
graph(300,300,-10,10,-10,10,0, 4, (-1/8)(x+2)^2 + 2))}}}
<u>See below descriptions of various conics                         </u>
Standard Form of an Equation of a Circle is {{{(x-h)^2 + (y-k)^2 = r^2}}} 
where Pt(h,k) is the center and r is the radius

 Standard Form of an Equation of an Ellipse is {{{(x-h)^2/a^2 + (y-k)^2/b^2 = 1 }}} where Pt(h,k) is the center. (a positioned to correspond with major axis)
 a and b  are the respective vertices distances from center and ±{{{sqrt(a^2-b^2)}}}are the foci distances from center: a > b

Standard Form of an Equation of an Hyperbola opening right and  left is:
  {{{(x-h)^2/a^2 - (y-k)^2/b^2 = 1}}} where Pt(h,k) is a center  with vertices 'a' units right and left of center.

Standard Form of an Equation of an Hyperbola opening up and down is:
  {{{(y-k)^2/b^2 - (x-h)^2/a^2 = 1}}} where Pt(h,k) is a center  with vertices 'b' units up and down from center.

the vertex form of a parabola opening up or down, {{{y=a(x-h)^2 +k}}} where(h,k) is the vertex.
The standard form is {{{(x -h)^2 = 4p(y -k)}}}, where  the focus is (h,k + p)

the vertex form of a parabola opening right or left, {{{x=a(y-k)^2 +h}}} where(h,k) is the vertex.
The standard form is {{{(y -k)^2 = 4p(x -h)}}}, where  the focus is (h +p,k )