题目

Traffic jams（堵塞）is a big problem in many big cities. Now, people use a “super bus”to solve the problem. The“super bus”is 40 meters long and 6 meters wide. It has two floors. Passengers（乘客）sit on the upper floor. A“super bus”can hold 1,200 to 1,400 people. That is the work of about 40 ordinary（普通的）buses. When the“super bus”runs on the road, the other cars and buses can run through from its low floor. That is just like boatsor ships go through a bridge. So the“super bus”hardly（几乎不）takes any room of the roads. So we can say using the“super在平面直角坐标系xOy中，抛物线y1=2x2+14的顶点为M，直线y2=x，点P（n，0）为x轴上的一个动点，过点P作x轴的垂线分别交抛物线y1=2x2+14和直线y2=x于点A，点B．（1）直接写出A，B两点的坐标（用含n的代数式表示）；（2）设线段AB的长为d，求d关于n的函数关系式及d的最小值，并直接写出此时线段OB与线段PM的位置关系和数量关系；（3）已知二次函数y=ax2+bx+c（a，b，c为整数且a≠0），对一切实数x恒有x≤y≤2x2+14，求a，b，c的值．