exam Maths Puzzle Numerical Ability

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

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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 (-3) 3pie - (-8)(-2)