Question 822153
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Hi,
{{{x=(1/2)(y+2)^2-(5/2)}}}  |  V(-5/2, -2), y = -2, line of symmetry
(y+2)^2 = 2(x+5/2), 4p = 2, p = 1/2  |Foci:  (-2,-2) & (-3,-2)
the vertex form of a Parabola opening right(a>0) or left(a<0), {{{x=a(y-k)^2 +h}}}
 where(h,k) is the vertex and  y = k  is the Line of Symmetry
The standard form is {{{(y -k)^2 = 4p(x -h)}}}, where  the focus is (h +p,k )
<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 variable 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 up and down is:
  {{{(y-k)^2/b^2 - (x-h)^2/a^2 = 1}}} with C(h,k) and vertices 'b' units up and down from center,  2b the length of the transverse axis
Foci {{{sqrt(a^2+b^2)}}}units units up and down from center, along x = h
& Asymptotes Lines passing thru C(h,k), with slopes m =  ± b/a

Standard Form of an Equation of an Hyperbola opening right and  left is:
  {{{(x-h)^2/a^2 - (y-k)^2/b^2 = 1}}} with C(h,k) and vertices 'a' units right and left of center,   2a the length of the transverse axis
Foci are {{{sqrt(a^2+b^2)}}} units right and left of center along y = k
& Asymptotes Lines passing thru C(h,k), with slopes  m =  ± b/a 


the vertex form of a Parabola opening up(a>0) or down(a<0), {{{y=a(x-h)^2 +k}}} 
where(h,k) is the vertex  and  x = h  is the Line of Symmetry
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(a>0) or left(a<0), {{{x=a(y-k)^2 +h}}}
 where(h,k) is the vertex and  y = k  is the Line of Symmetry
The standard form is {{{(y -k)^2 = 4p(x -h)}}}, where  the focus is (h +p,k )