已知:拋物線l
1:y=-x
2+2x+3交x軸于點(diǎn)A,B(點(diǎn)A在點(diǎn)B的左側(cè)),交y軸于點(diǎn)C,拋物線l
2經(jīng)過點(diǎn)A,與x軸的另一個(gè)交點(diǎn)為E(6,0),交y軸于點(diǎn)D(0,-3).
(1)求拋物線l
2的函數(shù)表達(dá)式;
(2)P為拋物線l
1的對(duì)稱軸上一動(dòng)點(diǎn),連接PA,PC,當(dāng)∠APC=90°時(shí),求點(diǎn)P的坐標(biāo);
(3)M為拋物線l
2上一動(dòng)點(diǎn),過點(diǎn)M作直線MN∥y軸,交拋物線l
1于點(diǎn)N,求點(diǎn)M自點(diǎn)A運(yùn)動(dòng)至點(diǎn)E的過程中,線段MN長(zhǎng)度的最大值.