题目内容
如图16，在平面直角坐标系中，直线
与
轴交于点
，与
轴交于点
，抛物线
经过
三点．
（1）求过三点抛物线的解析式并求出顶点
的坐标；
（2）在抛物线上是否存在点
，使
为直角三角形，若存在，直接写出点坐标；若不存在，请说明理由；
（3）试探究在直线
上是否存在一点
，使得
的周长最小，若存在，求出点的坐标；若不存在，请说明理由．
解：（1）
直线与轴交于点，与轴交于点．
，
························································································· 1分
点
都在抛物线上，
抛物线的解析式为
························································ 3分
顶点
······························································································· 4分
（2）存在··············································································································· 5分
············································································································· 7分
············································································································ 9分
（3）存在·············································································································· 10分
理由：
解法一：
延长
到点
，使
，连接
交直线于点，则点就是所求的点．
····················································································· 11分
过点作
于点
．
点在抛物线上，
在
中，
，
，
，
在
中，
，
，
，
··············································· 12分
设直线的解析式为
解得
································································································ 13分
解得
在直线上存在点，使得的周长最小，此时
．··· 14分
天天向上一本好卷系列答案
小学生10分钟应用题系列答案
如图1，在平面直角坐标系中，抛物线y=ax2+c与x轴正半轴交于点F（16，0），与y轴正半轴交于点E（0，16），边长为16的正方形ABCD的顶点D与原点O重合，顶点A与点E重合，顶点C与点F重合．
