Answer:
[tex]y=\frac{-1}{4}(x-1)^2-2[/tex]
Step-by-step explanation:
Given : focus of (1, -3) and a directrix of y= -1
The distance between focus and directrix is 2p
The distance between (1,-3) and y=-1 is 2
So 2p = 2 and p =1
Vertex (h,k) lies inbetween the focus and directrix
focus is (h, k-p)
given focus is (1,-3)
so h=1 and k-p = -3 ( we got p =1)
So k-1= -3 , k= -2
Hence, vertex is (1,-2), h=1 and k = -2
[tex]a=\frac{1}{4p} =\frac{1}{4}[/tex]
Here focus at the bottom and directrix at the top
so parabola opens down
hence a= -1/4
Plug it in the equation
[tex]y=a(x-h)^2+k[/tex]
[tex]y=\frac{-1}{4}(x-1)^2-2[/tex]
