问题 选择题
已知y1=a1x2+b1x+c1,y2=a2x2+b2x+c2且满足
a1
a2
=
b1
b2
=
c1
c2
=k(k≠0,1)
.则称抛物线y1,y2互为“友好抛物线”,则下列关于“友好抛物线”的说法不正确的是(  )
A.y1,y2开口方向、开口大小不一定相同
B.因为y1,y2的对称轴相同
C.如果y2的最值为m,则y1的最值为km
D.如果y2与x轴的两交点间距离为d,则y1与x轴的两交点间距离为|k|d
答案

由已知可知:a1=ka2,b1=kb2,c1=kc2

A、根据友好抛物线的条件,a1、a2的符号不一定相同,所以开口方向、开口大小不一定相同,故本选项错误;

B、因为

a1
a2
=
b1
b2
=k,代入-
b
2a
得到对称轴相同,故本选项错误;

C、因为如果y2的最值是m,则y1的最值是

4a1c1-b12
4a1
=k•
4a2c2-b22
4a2
=km,故本选项错误;

D、因为设抛物线y1与x轴的交点坐标是(e,0),(g,0),则e+g=-

b1
a1
,eg=
c1
a1
,抛物线y2与x轴的交点坐标是(m,0),(d,0),则m+d=-
b2
a2
,md=
c2
a2
,可求得:|g-e|=|d-m|=
b12-4a1c1
a12
,所以这种说法不成立的,故本选项正确.

故选D.

完形填空
Jennie sat at her window as usual, looking out upon the street, with a look of sadness on her face,“What a long day this is going to be!”
Then she saw a little boy running down the street, swinging his schoolbag. Looking up to the window, he took off    1   hat and bowed with a bright, pleasant smile.
“What a nice    2   ,”said Jennie to herself, as the boy ran out of sight.“It seems like having the sunshine. I wish everybody who goes by would look up    3   smile.”
George, the little boy, told his mother about that    4   girl when he got back home,“She looks so helpless. I wish I could do something for her.”
“Why not give her some    5  ?”said his mother. George agreed.
The next morning, as Jennie    6    at he window again, she saw George with a handful of beautiful flowers carefully picking his way across the street. He stopped in front of her window, smiling pleasantly, and said,“Can I come in?”Jennie told him    7   to get into the house.
Opening the door to Jennie’s gentle“Come in”, George said, “I’ve brought you some flowers.”
“Are they for me?”said Jennie    8  .“How kind you are,”she continued, as George put the flowers on her lap.“I’ve    9   received any flower since we moved to the town.”
“Did you live in the countryside?”asked George,    10    the old, small and empty room.
“Yes,”said Jennie.
Jennie used to have a happy family and live in a beautiful house in the countryside. However, she lost her right leg in an accident. She    11   walk like other people any longer. Later, her father died, and her mother was sick   12    so many years that their money was all gone. They sold the house, and move here to get work to do.
George told his parents    13   . They decided to help her. More and more people in the   14   gave Jennie friendly smiles when they passed by her house. She was greatly cheered up.
A few months later, Jennie and her mother    15   a flower shop. People could always see Jennie sitting in the shop, having a lovely smile on her face.
小题1:
A.herB.hisC.yourD.my
小题2:
A.houseB.doorC.smileD.schoolbag
小题3:
A.andB.butC.asD.or
小题4:
A.richB.luckyC.badD.poor
小题5:
A.moneyB.flowersC.clothesD.food
小题6:
A.dancedB.criedC.satD.laughed
小题7:
A.howB.whoC.whenD.why
小题8:
A.angrilyB.easilyC.sadlyD.happily
小题9:
A.neverB.usuallyC.alwaysD.sometimes
小题10:
A.looking forB.looking around
C.looking likeD.looking after
小题11:
A.shouldn’tB.needn’tC.couldn’tD.mustn’t
小题12:
A.forB.inC.atD.on
小题13:
A.somethingB.anythingC.everythingD.nothing
小题14:
A.countrysideB.townC.villageD.city
小题15:
A.reachedB.leftC.closedD.opened
计算题