Question 607345
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
y = x^2 + 6x - 4     This is a Parabola.
the vertex form of a parabola opening up or down, {{{y=a(x-h)^2 +k}}} where(h,k) is the vertex.
y = x^2 + 6x - 4    |Completing the Square
y = (x+3)^2-9-4
y = (x+3)^2 - 13    Vertex(-3,13) 
0 = (x+3)^2 - 13    | x = -3 ± sqrt(13), Roots -6.61 and .61 

{{{drawing(300,300,   -20,20,-20,20,   blue(line(-3,20,-3,-20))  
 grid(1),
circle(-6.61, 0,0.6),
circle(.61, 0,0.6),

graph( 300, 300,  -20,20,-20,20, 0,(x+3)^2-13  ))}}}

See below descriptions of various conics

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 and b  are the respective vertices distances from center and ±{{{sqrt(a^2-b^2)}}}are the foci distances from center

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 )