determing quadratic rules

http://i77.photobucket.com/albums/j5...enthesetwo.jpg

Between e, and f how do I know whether to use y= a(x-h)^2+k form, or ax^2 +bx +c form? And how do I work it out?

http://i77.photobucket.com/albums/j5...ars/quest3.jpg

And how do I work out this one step by step?

Quadratic Rules - h & k values

Does this mean that h & k will always be the x & y co-ordinates of the turning point, if the quadratic is written in the form y = a(x-h) squared + k??? Please clarify..Thanks, Rob