(2013•宜昌)如圖1,平面直角坐標(biāo)系中,等腰直角三角形的直角邊BC在x軸正半軸上滑動(dòng),點(diǎn)C的坐標(biāo)為(t,0),直角邊AC=4,經(jīng)過(guò)O,C兩點(diǎn)做拋物線(xiàn)y
1=ax(x-t)(a為常數(shù),a>0),該拋物線(xiàn)與斜邊AB交于點(diǎn)E,直線(xiàn)OA:y
2=kx(k為常數(shù),k>0)
(1)填空:用含t的代數(shù)式表示點(diǎn)A的坐標(biāo)及k的值:A
(t,4)
(t,4)
,k=
;
(2)隨著三角板的滑動(dòng),當(dāng)a=
時(shí):
①請(qǐng)你驗(yàn)證:拋物線(xiàn)y
1=ax(x-t)的頂點(diǎn)在函數(shù)y=
-x2的圖象上;
②當(dāng)三角板滑至點(diǎn)E為AB的中點(diǎn)時(shí),求t的值;
(3)直線(xiàn)OA與拋物線(xiàn)的另一個(gè)交點(diǎn)為點(diǎn)D,當(dāng)t≤x≤t+4,|y
2-y
1|的值隨x的增大而減小,當(dāng)x≥t+4時(shí),|y
2-y
1|的值隨x的增大而增大,求a與t的關(guān)系式及t的取值范圍.