Part 1 -
1. f(x) = 5(x-2)^2 + 4
axis of symmetry: x = 2
vertex: (2, 4)
2. f(x) = 12(x + 6)^2 - 5
axis of symmetry: x = -6
vertex: (-6, -5)
3. f(x) = 2x^2 + 8x - 7
axis of symmetry: x = -2
vertex: (-2, -15)
I have to go somewhere right now, but I will get back to you as soon as I can (probably within a couple of hours) to finish answering the rest of your questions.