如图，二次函数y=x²+bx+c的图象交x轴于A（﹣1，0）、B（3，0）两点，交y轴于点C，连接BC，动点P以每秒1个单位长度的速度从A向B运动，动点Q以每秒$\sqrt{2}$个单位长度的速度从B向C运动，P、Q同时出发，连接PQ，当点Q到达C点时，P、Q同时停止运动，设运动时间为t秒．

（1）求二次函数的解析式；

（2）如图1，当△BPQ为直角三角形时，求t的值；

（3）如图2，当t＜2时，延长QP交y轴于点M，在抛物线上存在一点N，使得PQ的中点恰为MN的中点，请直接写出N点的坐标．

——Which dress do you prefer? ——The red one. It _______ softer.

    There are times when people are so tired that they fall asleep almost anywhere.We can see there is a lot of sleeping on the bus or train on the1home from work in the evenings.A man will be2the newspaper,and seconds later it3as if he is trying to4it.Or he will fall asleep on the shoulder of the stranger5next to him.6place where unplanned short sleep7is in the lecture hall where a student will start snoring（打鼾）so 8that the professor has to ask another student to9the sleeper awake.A more embarrassing（尴尬）situation occurs when a student starts falling into sleep and the10of the head pushes the arm off the11,and the movement carries the 12of the body along.The student wakes up on the floor with no13of getting there.The worst time to fall asleep is when14.Police reports are full of15that occur when people fall into sleep and go16the road.If the drivers are 17,they are not seriously hurt.One woman's car,18,went into the river.She woke up in four feet of19and thought it was raining.When people are really20nothing will stop them from falling asleep—no matter where they

are.