题干

如图,已知抛物线y=ax2+bx+c(a≠0)的顶点坐标为(4,-
2
3
),且与y轴交于点C(0,2),与x轴交于A,B两点(点A在点B的左边).

(1)求抛物线的解析式及A、B两点的坐标;
(2)在(1)中抛物线的对称轴l上是否存在一点P,使AP+CP的值最小?若存在,求AP+CP的最小值,若不存在,请说明理由;
(3)以AB为直径的⊙M相切于点E,CE交x轴于点D,求直线CE的解析式.
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答案(点此获取答案解析)

解:(1)由题意,设抛物线的解析式为y=a(x﹣4)2
2
3
(a≠0)

∵抛物线经过(0,2)
∴a(0﹣4)2

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