SOLUTION: Identify vertex, focus, directrix, axis of symmetry and latus rectum from the following parabola equation: {{{x=(1/8)(y+1)^2+3}}}

Question 142052: Identify vertex, focus, directrix, axis of symmetry and latus rectum from the following parabola equation:

Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
Identify vertex, focus, directrix, axis of symmetry and latus rectum from the following parabola equation:

Two things you must know about parabolas, their graphs
and their equations
1. The parabola whose equation is

opens upward if p is positive, and downward if p is negative.
It has:
vertex, the point (h,k),
focus, the point (h,k+p),
directrix, the horizontal line whose equation is y=k-p
length of latus rectum = 4p,
endpoints of the latus rectum, the points (h-2p,k+p),(h+2p,k+p)
2. The parabola whose equation is

opens to the right if p is positive, and
to the left if p is negative.
It has:
vertex, the point (h,k),
focus, the point (h+p,k),
directrix, the vertical line whose equation is x=h-p
length of latus rectum = 4p,
endpoints of the latus rectum, the points (h+p,k-2p),(h+p,k+2p)
Your parabola is the second type:

Compare that to

so
so
so
It opens to the right because , a positive number.
It has:
vertex, the point (h,k) = (,)
focus, the point (h+p,k) = (,) = (,)
directrix, the vertical line whose equation is or or
length of latus rectum = = = =
endpoints of the latus rectum, the points (,) and (,), or (,) and ,)
The parabola looks like this. The vertical line is the directrix.
The focus is the little dot just inside the parabola. I won't try to
draw the latus rectum. It is a very short line, only of a
unit that goes across the parabola through the focus.

Edwin
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