题目

As an exchange student, Wei Hua studied in a British high school for one year. She was happy   41 the school hours in Britain because school starts around 9 a.m. and ends about 3.30 p.m. On the first day, all the new students   42 (attend) an assembly in the school hall. Wei Hua sat next to a girl 43 name was Diana. During the assembly, the headmaster told the students that the best way to earn respect was to devote themselves    44 study and achieve high 45 (grade). As there were different students in some classes,  46 was a struggle for Wei Hua to remember all the faces and n对于二次函数y=ax2+bx+c，如果当x取任意整数时，函数值y都是整数，那么我们把该函数的图象叫做整点抛物线（例如：y=x2+2x+2）．（1）请你写出一个二次项系数的绝对值小于1的整点抛物线的解析式________．（不必证明）（2）请探索：是否存在二次项系数的绝对值小于的整点抛物线？若存在，请写出其中一条抛物线的解析式；若不存在，请说明理由．