问题 填空题
已知二次函数y=ax2+bx+c的图象与x轴交于(1,0)和(x1,0),其中-2<x1<-1,与y轴交于正半轴上一点.下列结论:①b>0;②ac<
1
4
b2
;③a>b;④-a<c<-2a.其中所有正确结论的序号是______.
答案

∵抛物线与x轴的交点为(1,0)和(x1,0),-2<x1<-1,与y轴交于正半轴,

∴a<0,

∵-2<x1<-1,

∴-

1
2
<-
b
2a
<0,

∴b<0,b>a,故①错误,③错误;

∵抛物线与x轴有两个交点,

∴b2-4ac>0,

∴ac<

1
4
b2,故②正确;

∵抛物线与x轴的交点有一个为(1,0),

∴a+b+c=0,

∴b=-a-c,

∵b<0,b>a(已证),

∴-a-c<0,-a-c>a,

∴c>-a,c<-2a,

∴-a<c<-2a,故④正确,

综上所述,正确的结论有②④.

故答案为:②④.

阅读理解

阅读理解。

      A man went to a fast-food restaurant to buy his lunch."Hi," a worker said."May I help you?"

     "I'd like a hamburger, large chips, and a Coke," the man said.

     "Anything else?" the worker asked.

     "No," the man answered."That's it."

     "Is that for here or to go?" The worker asked.

     "To go," the man said.

     The worker put the man's lunch in a bag. The man took out his money and paid for his lunch.

     "Thank you," the worker said. "Have a nice day."

      The man took the bag and walked to a park. He sat down and opened the bag. He was surprised.

There was no hamburger in the bag. There were no chips. There was no Coke. There was only money

in the bag-a lot of money! The man counted the money. Two thousand dollars! Why was the money in the

bag? Where was the man's lunch?

     The manager of the fast-food restaurant needed to go to the bank. He put two thousand dollars in an

envelope (信封). He put the envelope in a bag and put the bag down. The worker gave the manager's bag to

the man by mistake. So the manager had a hamburger, chips and a Coke, and the man had two thousand

dollars. What should the man do?

1. The man went to a restaurant to __________.

A. buy his lunch

B. have a rest

C. sell drinks

D. cook food

2. The man wanted to have his lunch __________.

A. in a hotel

B. in a shop

C. in a restaurant

D. in a park

3. When the man opened the bag, he found __________ in it.

A. food

B. drink

C. money

D. nothing

4. _________ couldn't find his money.

A. The man

B. The manager

C. The worker

D. Nobody

单项选择题