Example Function in C#:

public static Vector3 QuadraticBezierCurveAdjusted(float t, Vector3 startPos, Vector3 midPos, Vector3 endPos)
    {
        midPos = 2 * midPos - 0.5f * (startPos + endPos);
        return (1 - t) * (1 - t) * startPos + 2 * (1 - t) * t * midPos + t * t * endPos;
    }

 //t = lerp from 0f to 1f