问题 解答题
某校研究性学习小组在研究有关二次函数及其图象性质的问题时,发现了两个重要的结论:一是发现抛物线y=ax2+2x+3(a≠0),当实数a变化时,它的顶点都在某条直线上;二是发现当实数a变化时,若把抛物线y=ax2+2x+3的顶点的横坐标减少
1
a
,纵坐标增加
1
a
,得到A点的坐标;若把顶点的横坐标增加
1
a
,纵坐标增加
1
a
,得到B点的坐标,则A、B两点一定仍在抛物线y=ax2+2x+3上.
(1)请你协助探求实数a变化时,抛物线y=ax2+2x+3的顶点所在直线的解析式;
(2)问题(1)中的直线上有一个点不是该抛物线的顶点,你能找出它来吗?并说明理由.
答案

(1)y=ax2+2x+3=a(x+

1
a
)2+3-
1
a

抛物线y=ax2+2x+3的顶点坐标为 (-

1
a
,3-
1
a
),

∴抛物线y=ax2+2x+3的顶点所在直线的解析式为y=x+3;

(2)当a≠0时,顶点的横坐标-

1
a
≠0,

∴(0,3)点不是抛物线的顶点.

阅读理解

Part I: _________________________                 

If you are hunting a chance to improve yourself in English, TOP ENGLISH CITY will be a smart choice.We are members of "the International Language Workshop" and enjoy both of the good honor in English teaching and high quality of our teaching team.We provide affordable, excellent English training programs for those who want to improve both their English knowledge and their language skills.

In TOP ENGLISH CITY, you will be a top English-speaker among your competitors and enjoy the advantage that your competitors have not.You will be proud of being a member of TOP ENGLISH CITY.

Courses designed:

Basic Studies:Sat.8:00-10:00 a.m.

Intermediate(中级)Spoken English: Sun.8:00-10:00 a.m.

Standard Spoken English: Sat.8:00-10:00 a.m.

Basic Business English: Sun.8:00-10:00 a.m.

Intermediate Business English: Sun.7:00-9:00 p.m.

TOEFL Super Studies… Sun.7:30-9:30 p.m.

Children's Weekend: Sat.&.Sun.8:00 a.m. -5:00 p.m.

For more information, please contact:

Room 807 American Plaza Tianhexi Rd, 510150 Guangzhou

Tel: 86668888-8807

Part II : ENGLISH SALON

A place for you to practise your English, to exchange your English learning experiences, to know more about the culture of English-speaking countries, to make more friends who can speak very good English.

You will have free talks, famous English films and songs appreciation, English lectures and games; all are for you to improve yourself in English in the special, full-of-fun Salon.

How to Join:

We are a group with membership system, so if you want to join our group, please make an application to the Tianhe Office of Top English City, filling in the applying forms.You will be given a salon ID card, and becomes our member.

The Qualifications:

You must be fluent in English-speaking or / and an English lover.Those who are now learning English in the Top English City will be advantageous.

For more information, please contact:

Mr. Jiu Chan    at: 47129198 English Salon, your best friend! Join Right Now!

小题1:Which of the following can be the best title for Part I?

A.Top English, your smart choice!

B.If you want to learn English, we can teach you!

C.Top English, the best English!

D.We have what you want!小题2:Which of the following courses can be learned by the same person________?

A.Basic Studies and Standard Spoken English.

B.Intermediate Spoken English and Basic Business English.

C.Standard Spoken English and TOEFL Super Studies.

D.Intermediate Business English and TOEFL Super Studies.小题3: If you work in a foreign firm, you probably take the course______.

A.Standard Spoken English

B.Intermediate Business English

C.TOEFL Super Studies

D.Children's Weekend小题4: If you want to join the English Salon, you should at least ________.     

A.be a university graduate

B.be a student learning English in the Top English City

C.make more friends and know more about the culture of the English

D.be an English lover or can speak English well

单项选择题 B型题