如圖,已知拋物線的解析式為y=-
x
2-
x+3,拋物線與x軸交于點(diǎn)A和點(diǎn)B,與y軸交點(diǎn)于點(diǎn)C.
(1)請(qǐng)分別求出點(diǎn)A、B、C的坐標(biāo)和拋物線的對(duì)稱(chēng)軸;
(2)連接AC、BC,將△ABC繞點(diǎn)B順時(shí)針旋轉(zhuǎn)90°,點(diǎn)A、C的對(duì)應(yīng)點(diǎn)分別為M、N,求點(diǎn)M、N的坐標(biāo);
(3)若點(diǎn)P為該拋物線上一動(dòng)點(diǎn),在(2)的條件下,請(qǐng)求出使|NP-BP|最大時(shí)點(diǎn)P的坐標(biāo),并請(qǐng)直接寫(xiě)出|NP-BP|的最大值.