To get the equation, you will need a vertex. You can find the vertex from knowing the focus and directrix. The vertex’s position is halfway between the directrix and the focus. See graph. The midpoint between (1,1) and (1,2) is (1, 1.5). Therefore, the vertex is (1, 0.5) where h=1 and k=1.5
Another thing you know is the parabola will be upside down. It’s general formula is (x-h)2=4p(y-k).
p is the distance between the vertex and focus, which is -0.5. Therefore 4p is -2.
Your final equation is
(x-1)2=-2(y-1.5)
Type this equation in Desmos.com/calculator, and you will see what it looks like. The vertex will be between the focus and directrix.
