You want it to look like this
which is a parabola with a horizontal axis of symmetry that
either opens left or right. We can't tell which yet. It
has a vertex of (h,k)
Get the y-terms on the left and everything else on the right
Divide every term by 4
Complete the square on the left side:
1. To the side, multiply the coefficient of y, which is -1, by 
,
getting 
2. Square the result of 1. 
3. Add the result of 2 to both sides of the equation:
Factor the left side: 
Combine the numbers on the right 
To show the 4p in the standard equation, perhaps your teacher
wants you to put a 1 factor on the right side:
and now it corresponds exactly to
The vertex is (h,k) = (1,)
4p=1, so p=
, since p is positive it opens right.
Its focus is the point unit right of its vertex,
at (1,
), and the latus rectum is 4p=1 unit long
through the focus. The directrix line is the vertical
line unit left of the vertex. It has the
equation 
. to 4p = 1 unit. So we draw the
vertex, focus, directrix and latus rectum and we have this:
Then we sketch in the parabola:
Yes, I know you didn't need to graph it but you'll have to later.
Edwin
