According to Wikipedia, a quadratic Bezier curves are given by begin/end points , and a control point, :
From there, I let , and , giving
Thus one normal would be , and
the signed curvature is .
Note: is just a vector way of writing .
I also pulled the formula for the signed curvature off wikipedia, though that should be easy to find everywhere.
I certainly could have made a mistake somewhere, so I'd suggest you work it out yourself. If you get the same thing, then it's a good bet neither of us made a mistake.