请按照上海初三学生的水平，讲解这道题目---```plain
2、在平面直角坐标系xOy中，已知抛物线y = ax^2 + bx + 3经过点A(1,0)、B(-2,3)两点，与y轴的交点为C点，对称轴为直线l.
(1)求此抛物线的表达式;
(2)已知以点C为圆心,半径为CB的圆记作圆C, 以点A为圆心 的圆记作圆A, 如果圆A与圆C外切,试判断对称轴直线l与圆A的位置关系, 请说明理由;
(3)已知点D在y轴的正半轴上,且在点C的上方,如果∠BDC = ∠BAC,请求出点D的坐标.
Chart Description:
Type: Cartesian coordinate system.
Main Elements:
- X-axis: Horizontal line with an arrow pointing to the right, labeled 'x'. Marked points are -1, 0, 1.
- Y-axis: Vertical line with an arrow pointing upwards, labeled 'y'. Marked points are -1, 0, 1.
- Origin: The intersection of the x and y axes, implicitly labeled as 0.
- Grid lines: Short ticks are present on both axes indicating integer units.
- The coordinate system provides a visual reference for plotting points and understanding the geometry described in the problem.
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