Question 621670
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
What is the graph of
f(x)=1/3(x-4)^2-1   Parabola Opening up along x = 4, V(4,-1)

{{{drawing(300,300,   -6, 6, -6, 6,  blue(line(4,6,4,-6))  , grid(1),
circle(4, -1,0.3),
graph( 300, 300, -6, 6, -6, 6,0, (1/3)(x-4)^2-1 ))}}}
<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 
and foci {{{sqrt(a^2+b^2)}}} units right and left of center along y = k

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, 
and foci {{{sqrt(a^2+b^2)}}}units units up and down from center, along x = h

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.
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.
The standard form is {{{(y -k)^2 = 4p(x -h)}}}, where  the focus is (h +p,k )