Her's a checlklst to help you with these [ this just applies to parabolas opening upward/downward]
1. Look at the y coordinate of the focus.....fi its numerical value is greater than that of the directrix, the parabola opens upward......if its value is less....the parabola opens downward.....this latter situation also implies that we will have a negative sign involved in our equation
Since 1 < 5....this opens downward
2. Find the vertex.....for parabolas opening upward/downward.....the x coordinate of the focus = the x coordinate of the vertex......so.....we only need to determine the y coordinate of the vertex....to do this.....add the diectrix value and the y coordinate of the focus and divide this sum by 2......so we have [ 5 + 1]/ 2 = 6/2 = 3
So....the vertex = ( 2, 3) = (h, k)
3. Find "p".....this is the distance between the focus and vertex.....again.....we are just concerned with the y coordinates of the vertex and focus.....to find p, take the absolute value of their difference.....so we have
l 3 - 1 l = l 2 l = 2
So......we have the form
4p (y - k) = -(x - h)^2 note the "- " ....now.... fill in what we know
4 (2) (y - 3) = -(x - 2)^2
8 ( y - 3) = - (x -2)^2 multiply both sides by 1/8
(y - 3) = -(1/8) ( x - 2)^2 add 3 to both sides
y = -(1/8)(x - 2)^2 + 3