(x-h)^2=4p(y-k) vertex is (h,k) p is the distance from focus to vertex and distance from vertex to directix (vertex is in middle of directix and focus) if p is positive, the parabola opens up and the focus is above the directix if p is negative, the parabola opens down and the focus is below the directix
we see the directix is over the focus (1>-1) so the parabola opens down and p is negative distance from (5,-1) to y=1 is 2 units 2/2=1 p=-1 since p is negative 1 up from (5,-1) is (5,0) veretx is (5,0) (x-5)^2=4(-1)(y-0) (x-5)^2=-4y is the equation
The answer is <span>directrix is horizontal, so the parabola is vertical </span> <span>focus lies below the directrix, so the parabola opens downwards. </span>
<span>Apply your data and solve for h, k, and a. </span> <span>vertex is halfway between focus and directrix: (3,3) </span> <span>h = 3 </span> <span>k = 3 </span>
<span>distance between focus and vertex is 2, so p = 2. </span> <span>a = -1/(4p) = -⅛ </span>