According to Wikipedia, a quadratic Bezier curves are given by begin/end points , and a control point, :

.

From there, I let , and , giving

, and

.

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.