Parabolas: What's the Point?

Algebra Level 3

For any real number α \alpha, the parabola fα(x)=2x2+αx+3α f_\alpha (x) = 2x^2 + \alpha x + 3 \alpha passes through the common point (a,b) (a, b) . What is the value of a+b?a+b?

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