题目

D For John and Amy Cervantes, birthdays have always been a big deal — a welcome excuse to celebrate life. When their eldest son, Alex, turned three, in 2005, they invited 20 friends to a nearby park and hired a clown to paint faces and make balloon animals.     Not long after that, the couple were brainstorming ways to teach Alex about giving to others. “That’ s when a spark went off,” says Amy. “We wanted to do something that would have a strong effect on our community, that wasn’t already being  done, and that our young children could participate in. I started wondering what （2006•茂名）已知：半径为1的⊙O1与x轴交于A、B两点，圆心O1的坐标为（2，0），二次函数y=-x2+bx+c的图象经过A、B两点，其顶点为F．（1）求b、c的值及二次函数顶点F的坐标；（2）写出将二次函数y=-x2+bx+c的图象向下平移1个单位再向左平移2个单位的图象的函数表达式；（3）经过原点O的直线l与⊙O相切，求直线l的函数表达式．