(1) You can use differentiation or complete the square like you did . Yes , its vertex .. or in other words max or min points .
(2) Ok ..
You will get a U shaped graph where it intersects x=10 and x=-2 .
y is less than or equals 0 ... so the solution part will be the lower part of the U graph because the lower part of the graph has all its values of y lesser than 0 ..
Did i make things confusing for you ?