Who can help me with this Calculus question?

f(x) = (4/x) + 2

g(x) = ax^2 + bx + c

f(x) and g(x) intersect and have a common tangent at point B with x = 2.

f(x) and g(x) also intersects at point A(1, 6)

find the vertex of the parabola,

find a, b and c