问题 解答题

已知二次函数y=ax2+bx-3的图象经过点A(2,-3),B(-1,0).

(1)求二次函数的解析式;

(2)填空:要使该二次函数的图象与x轴只有一个交点,应把图象沿y轴向上平移______个单位.

答案

(1)由已知,有

4a+2b-3=-3
a-b-3=0
,即
4a+2b=0
a-b=3
,解得
a=1
b=-2

∴所求的二次函数的解析式为y=x2-2x-3.

(2)∵-

b
2a
=1,
4ac-b2
4a
=-4.

∴顶点坐标为(1,-4).

∵二次函数的图象与x轴只有一个交点,

∴应把图象沿y轴向上平移4个单位.

阅读理解

阅读短文,根据其内容回答问题。

These days, many Chinese people are happy about a piece of news. What is it? China may become the second largest economy (经济体) in the world. It’s only behind the US.

But is China the second richest country, too?

No. The economy is like a cake. The US, Japan and China each makes one. China makes the second biggest cake. But lots of people have to eat it. Why? There are 1.3 billion people in China. And there are only 300 million people in the US and 127 million in Japan. So, in China, each person only gets a very, very small piece of cake. But people in the US and Japan have bigger pieces.

China is not as rich as the US and Japan. For example, in the US, in every 100 people, 75 can surf the Internet; in Japan it is 74 in 100. But in China, only 26 people in 100 use the Internet.

China’s large economy brings good things. People in China have more jobs and money. We also have more influence (影响) in the world.

小题1:China is the second largest economy in the world, isn’t it?

                                                     

小题2:Why isn’t China as rich as the US and Japan?

                                                     

小题3:How many people in 100 can use the Internet in China?

                                                     

小题4:Who can get bigger pieces of cake, Chinese or Americans?

                                                      

小题5:China’s large economy brings good things. What are they?

                                                      

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