配套习题- 二次函数压轴题——线段和的最小值问题（二） -【青果学院】

1/5单选题

难度：

1.已知，在平面直角坐标系xoy中，点A的坐标为（0，2），点P（m，n）是抛物线y=

+1上的一个动点. 如图1，过动点P作PB⊥x轴，垂足为B，连接PA，则有结论：PA=PB。如图2，设C的坐标为（2，5），连接PC，则AP+PC取得最小值时点P的坐标为（）

A	（1，）
B	（2，2）
C	（3，）
D	（0，1）

正确答案：Qg==

6Kej77ya6L+H54K5UOS9nFBC4oqleOi9tOS6jkLvvIznlLHvvIgx77yJ5b6XUEE9UELvvIw8YnI+5omA5Lul6KaB5L2/QVArQ1DmnIDlsI/vvIzlj6rpnIDlvZNCUCtDUOacgOWwj++8jOWboOatpOW9k0PvvIxQ77yMQuWFsee6v+aXtuWPluW+l++8jDxicj7mraTml7bngrlQ55qE5qiq5Z2Q5qCH562J5LqO54K5Q++8iDLvvIw177yJ55qE5qiq5Z2Q5qCH77yMPGJyPuaJgOS7peeCuVDnmoTlnZDmoIfkuLrvvIgy77yMMu+8ie+8jDxicj7mlYXpgIlC44CC

2/5单选题

难度：

2.如图，以矩形OABC的顶点O为原点，OA所在的直线为x轴，OC所在的直线为y轴，建立平面直角坐标系. 已知OA=3，OC=2，点E是AB的中点，在OA上取一点D，将△BDA沿BD翻折，使点A落在BC边上的点F处. 在x轴、y轴上分别存在动点M、N，则四边形MNFE的周长最小值是（）。

A	5-
B	5+
C	5+
D	3+

正确答案：Qw==

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

3/5单选题

难度：

3.

已知：直线l：y=-2，抛物线y=x²−1经过点（0，-1），（2，0）. 如图①，点P是抛物线上任意一点，过点P作直线l的垂线，垂足为Q，已知PO=PQ；过原点作任意直线AB，交抛物线y=x²−1于点A、B，分别过A、B两点作直线l的垂线，垂足分别是点M、N，连结ON、OM，已知ON⊥OM. 点D（1，1），求抛物线上使得FD+FO取得最小值时点F的坐标为（）

A	（1，）
B	（2，）
C	（）
D	（1，- ）

正确答案：RA==

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

4/5单选题

难度：

4.已知，如图，二次函数y=ax²+bx+c（a≠0）的图象与y轴交于点C（0，4）与x轴交于点A、B，点B（4，0），抛物线的对称轴为x=1. 直线AD交抛物线于点D（2，m），直线AD与y轴交于点F，点M为抛物线对称轴上的动点，点N在x轴上，当四边形CMNF周长取最小值时，点M和点N的坐标分别是（）.

A	（1，1）、（，0）
B	（1，）、（，0）
C	（1，1）、（，0）
D	（1，）、（，0）

正确答案：QQ==

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

5/5单选题

难度：

5.已知：如图，在平面直角坐标系中，⊙P的圆心P（3，0），半径为5，⊙P与抛物线y=ax²+bx+c（a≠0）的交点A、B、C刚好落在坐标轴上. 点F是点C关于对称轴PD的对称点，若直线AF交y轴于点K，点G为直线PD上的一动点，点H是x轴上一动点，使C、G、H、K四点所围成的四边形周长最小时，对点G、H的坐标以及这个四边形周长最小值表达正确的是（）。

A	G(3，﹣)，H(，0)，四边形CGHK的最小周长l＝2+.
B	G(3，)，H(，0)，四边形CGHK的最小周长l＝3+.
C	G(3，)，H(，0)，四边形CGHK的最小周长l＝3+.
D	G(3，)，H(，0)，四边形CGHK的最小周长l＝2+.

正确答案：Qg==

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