Question

find the vertex, focus, line of symmetry, directrix, and x and y intercepts for (x+2)^2=12(y-1)

Answer 1

\[(x+2)^2=12(y-1)\] looks a lot like
\[(x-h)^2=4p(y-k)\] we just need to identify \((h,k)\) the vertex, and also \(p\)

Answer 2

you got the vertex? we need that first

Answer 3

the vertex is (-2,1)

Answer 4

and p is 3?

Answer 5

yes, and yes

Answer 6

now that you have the vertex, and see that the parabola opens up
you know the directrix is 3 units below the vertex (that is why you need the vertex and \(p\) first)

Answer 7

3 units below \((-2,1)\) puts you at \(y=-2\) and that is the directrix

Answer 8

the focus is 3 units up from the vertex, at \((-2,4)\)