⑴抛物线y=(t+1)+2(t+2)x+3/2的对称轴是x=1,
即-2(t+2)/[2(t+1)]=1,t=-3/2,
∴Y=-1/2X^2+X+3/2,
⑵Y=-1/2(X-1)^2+2,顶点坐标:(1,2),
顶点(1,2)向右再向下各平移2个单位后为(3,0),
∴Y=-1/2(X-3),即Y=-1/2X^2+3X-9/2.
⑶将新抛物线Y=1/2(X-3)^2,当顶点坐标在Y=-1/2X^2+X+3/2上运动时,
设顶点坐标为(m,-1/2m^2+m+3/2),
∴Y=1/2(X-m)^2-1/2m^2+m+3/2
=1/2X^2-mx+1/2m^2-1/2m^2+m+3/2
=1/2X^2-mX+m+3/2
当X=1时,Y=1/2-m+m+3/2=2,
即新抛物线过(1,2)即过原抛物线 的顶点.