问题 解答题

设二次函数y=﹣x2+4x﹣3的图象与x轴交于A,B两点,顶点为C.

(1)求A,B,C的坐标;

(2)在y轴上求作一点M,使MA+MC最小,并求出点M的坐标.

答案

解:(1)∵y=﹣x2+4x﹣3=﹣(x﹣2)2+1,

∴顶点C(2,1),

令y=0.即﹣(x﹣2)2+1=0,

∴(x﹣2)2=1,x﹣2=±1,x=3或1,

∴函数与x轴交点坐标为(3,0)或(1,0),

∴A(3,0),B(1,0),C(2,1)或A(1,0),B(3,0),C(2,1);

(2)①当A坐标为(3,0)时,A关于y轴对称点A'(﹣3,0),

设A'C的解析式为y=kx+b,

∴k=,b=

∴A'C的解析式为y=x+,与y轴交点为M(0,),

∴M在y轴上,使MA+MC最小时M点坐标为(0,);

②当A坐标为(1,0)时,同理可求得M坐标为(0,

∴满足题意的M点坐标为(0,)或(0,).

单项选择题
阅读理解

A public high school in the rural town of Boonsboro,Maryland,offers a special program recently. Top students in the ninth and tenth grades can attend single-sex classes for math,science,English and social studies.

The aim is to help teenagers keep their mind on their work by keeping males and females apart. Rebecca Brown chooses the students for what Boonsboro High School calls the Academy. “What we really want to do is take that top group of kids and take them to the very highest level they can achieve here,so that they’re prepared for college,” she said. They need high marks and test scores and strong teacher recommendations. They also need to be involved in activities.

Michael Bair has been at Boonsboro High School for twenty years and directs the Academy. His ninth-grade English class for boys centers on books that he believes boys find interesting. “The novels they’re reading now,are very manly novels. They’re novels that deal with the arrogance(傲慢)of man and the pride of man.” One of those books,for example,is “The Call of the Wild” by Jack London. This classic story tells of a dog stolen from his home and sold to work as a sled dog in Canada’s Klondike Gold Rush.

On this day,the students are working in small groups. Vincent and Logan explain why they’re drawing pictures that relate to the story. Vincent said,“The main character,Buck,gets abducted(绑架), and they send him off to the Yukon in a train. So I’m drawing part of the story where he’s in the train. It gets you to visualize the setting of the story and gets you to think more about what’s going on in the story,the important events of the story.”“ Instead of just doing work sheets about it,this is a lot more fun,” Logan added happily.

Morgan Van Fleet likes being in the Academy. She says boys and girls act differently when they are together in a classroom. “To me,it almost seems like it’s hindering(妨碍) your chances at developing yourself because you’re more focused on ‘Oh,I wish they’d shut up. Oh,what do they think of me?’ instead of focusing on what’s the homework or what’s going on in this class,what’s the lesson.”

小题1:What is the purpose of the text?

A.To educate.

B.To persuade.

C.To instruct.

D.To introduce.小题2:In Rebecca Brown’s opinion,________.

A.any student in Boonsboro High School can take part in the program

B.students in the program are expected to get well prepared for college

C.students can all achieve their highest levels in the program

D.students don’t have to join in the activities.小题3:The underlined word “visualize” in Paragraph 4 probably means “________”.

A.form a picture of

B.pay a visit to

C.take a look at

D.have a gift for小题4:What can we conclude from the text?____________.

A.Michael Bair considers it unsuitable for boys to read the book “The Call of the Wild”.

B.Vincent thinks that his drawings can help understand the novel better.

C.Jack London is a main character in the book “The Call of the Wild”.

D.Morgan Van Fleet thinks the program does no good to her.小题5:The text is probably taken from________.

A.a school’s introduction

B.a teacher’s diary

C.a headmaster’s speech

D.a news report