Book Maths Puzzle Quadratic Equations

what is the vertex of the quadratric equation y = x^2 - 6x + 9

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I need how to solve and verify the solutions:
1. r+7>-5
2. -35 +6n<7n
3. -14+p>4-(-2p)
4. x-5>-3/3
5. 4(n-1)<7n+8 A large awning is being designed for a hotel entrance and drive. The roof is to be a section of a parabola, with the vertex attached to the hotel wall 16 feet above the ground, and supported by 10 foot wall posts that are 12 feet away from the hotel wall.
Come up with a general equatation of a quadratic function that would model the roof of the awning.

Thanks for ANY help. I'm completely stuck on how to go about this problem algebraically.

Noelle
marknoni@comcast.net