vertex form: f(x) =a(x-h)^2 +k
f(x) =a(x-1)^2 +8
find a by putting in (3,-4) for x, f(x)
-4=a(3-1)^2 +8
-4 =4a+8
4a=-12
a=-3
f(x) =-3(x-1)^2 +8
you can put in any number for x and get f(x)
f(x) -3(0-1)^2 +8 = -3+8 =5
so (0,5) is another point
without finding the equation, since (1,8) is the vertex and x=1 the axis os symmetry , on the other side of the axis is the point (-1,-4)