exam Maths Puzzle Numerical Ability

This is tricky for me, A parabola has a vertical axis and passes through the points (0,3), (1,7) and (-2,-17). Find the equation of the parabola. use y=ax^2+by+c

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Can you please help?
Solve the system by substitution or elimination
a)....2/x+3/y=16
-1/x+2/y=6

b)....solve for x
|x...3..|
|2...x+1| }all = DET 16

c)...x^2+y^2=7 2^2x - 12(2^x) + 32 = 0

I know the answers are 2 and 3 but I do not know how to prove it algebraically