一元二次方程的解法PPT课件
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24
4
即 (x 1)2 49 4 16
开平方得: x 1 7
44
∴原方程的解为: x1 2 ,
x2
3 2
反馈练习巩固新知
1、用配方法解下列方程:
(1)x2+8x-15=0 (3)2x2-5x-6=0
(2)x2-5x-6=0 (4) x2+px+q=0(p2-4q> 0)
课堂小结布置作业
P7
Greek army has left and his captain
P8-9
Confirms it. The soldier found a huge, wooden
horse outside their city, and the captain
orders it to be moved into the city.
小结:
1、配方法:通过配方,将方程的左边化成一个含未
知数的完全平方式,右边是一个非负常数,运用直接
开平方求出方程的解的方法。 2、用配方法解一元二次方程 ax2+bx+c=0(a≠0) 的步骤:(1)化二次项系数为1 (2)移项
(3)配方(4)开平方(5)写出方程的解
pyramid 金字塔
Stonehenge 巨石阵
3.It was too big for them to take with them. =It was so big that they couldn’t take it with them.
take bring carry 随身携带
4. They all went to sleep, including the gate guards. The band played many songs, including some of my favorite. 十个人出席了会议,包括我爸爸。
左边:所填常数等于一次项系数一半的平方.
合作交流探究新知
问题: 要使一块矩形场地的长比宽多6m,并且 面积为16m2, 场地的长和宽应各是多少?
(1)解:设场地宽为X米,则长为(x+6)米,根据题意得:
X(X+6) = 16 整理得:X2+6X-16 = 0
x 2 6 x 16 0
移项
x 2 6 x 16
aptured
1.大木马
a huge wooden horse
2. 举行一次比赛 have\ hold\ run a competition
3. 冲下台阶
rush down the stairs
4.一会儿后
seconds later
5.朝下看
look down at
6. 再多等一小时 wait for another hour=wait for one more hour
大胆试一试:
填上适当的数或式,使下列各等式成立.
(1) x2 6x 32 =( x+ 3)2 (2) x2 8x 42 =( x 4)2
观察(1)(2)看所填的常 数与一次项系数之间
有什么关系?
(3) x2 4x 22=( x 2 )2
(4) x2 共同点:
px
(
p 2
)2=(
x
p
2 )2
3. What did the captain think about the horse? The captain thought that they had won the war.
He thought it was too big for the Greeks to take.
4.What did the citizens of Troy do that night?
Yes. (answers vary.)
Part B Look and think
These pictures show some of the events in the story on Page 58. Arrange them in the correct order.
Answers: c d b a f e
They celebrated their success.
5.Where did the six Greek soldiers hide ?
They hid in the horse.
6. Did the horse have something to do with the trick? How?
the Trojan War told in Hom荷er马’s I伊li利ad亚特 and Od奥ys德se赛y.
the prince of Troy fell in love with Helen, the queen of Sparta. 斯巴达
He k绑id架napped her and took her to Troy. All the Greek went to bring her back.
(1) seconds later = after a while 一会儿后(几秒钟后) (2) the city of Troy 特洛伊城
the city of Shenzhen=Shenzhen city
(3) look out = be careful look for 寻找 look after 照顾 look over = examine look down upon sb 看不起某人 look up to 看得起,尊重
Ten members are present at the meeting, including my father. 5. By midnight, the square was empty, except for the giant horse.
except for: not including 除 …之外(不包括) Except for one old lady, the bus was empty. 比较: We go to school every day except Saturday and Sunday. We have winter holiday besides summer holiday.
Read the passage and then answer the following questions
1.How was the soldier probably feeling when he came down the stairs, surprised or peaceful?
2. What did the captain think when he saw the empty plain?
It was a huge wooden horse.
2T.hHoewy dwidotnhethGereewkas rwwinitthhe awatrr?ick.
Read through the whole passage and match the main idea for each part.
7.进入城里
enter the city= get into city
8. 拿走,带走 take away
9. 除…之外
except for
10.拖…进城
pull / drag… into the city
Useful expressions
1.A newspaper ran a short competition on famous tales from history.
3. What did the captain think about the horse?
4.What did the citizens of Troy do that night?
5.Where did the six Greek soldiers hide ?
6.Did the horse have something to do with the trick? How?
一元二次方程的解法 ---配方法2
创设情境 温故探新
开心练一练:
1、用直接开平方法解下列方程: (1) 9x2 1
(2) (x 2)2 2
静心想一想:
2、下列方程能用直接开平方法来解吗?
(1) x2 4x 4 3
(2) X2+6X+9 = 2
把两题转化成 (x+b)2=a(a≥0)的 形式,再利用开平 方
compete (v)比赛---- competition competitor competitive
(n.)比赛 (n.)比赛者 (adj.) 比赛的
2. Seconds later, the captain stood on the high wall of the city of Troy, and looked down at the empty plain.
P1-2
The Trojans celebrate their victory
and then go to sleep.
P3-6
The Greek soldiers inside the horse open the city gates and let in the Greek
army. The Greek army capture Troy. A Trojan soldier announces that the
两边加上32,使左边配成
x2 2bx b2的形式
x 2 6 x 32 16 32
左边写成完全平方形式
( x 3)2 25
降次
x 3 5
x 3 5, x 3 5
得 : x 2, x 8
1
2
心动 不如行动
例1: 用配方法解方程
x2 6x 7 0
解: 移项得:x2 6x 7
the war lasted for ten years.
The night of the horse
Look at the title, the picture and the last paragraph, and then answer the two questions.
1. What kind of horse it is?
Summary The war between the Troy and the Greeks lasted ten years. At last, the Greeks won the war with a t___. They pretended to leriacvke the city of Troy, but they left a huge w______ horse behind. The Troy thought tohoeydehanve w__ the war so they c________, making j____ abouotnthe Greeks. Theeylewbereatseodhappy about othkeeirswin that all of them went to sleep, i________ the gate guard. The Greek soldiers i_____ the wooden horse opennceldutdhienggate and let their army in. In this way, they c_____ thnesTidroey city.
配方得:x2 6x 32 7 32
即 (x 3)2 16
开平方得: x 3 4
∴原方程的解为:x1 1, x2 7
范例研讨运用新知
例2: 你能用配方法解方程
2x2 x 6 0 吗?
解:化二次项系数为1得:x2 1 x 3 0
2
移项得: x2 1 x 3
2
配方得:x2 1 x (1)2 3 (1)2
Read the passage and then answer the following questions
1.How was the soldier probably feeling when he came down the stairs, surprised or peaceful?
2.HWe hparot bdaidbltyhewcaaspfteaeinlintghisnukrwprhiseendh. e saw the empty plain?
wheel 车轮
golden sunlight. 金色阳光
army 军队
Tian’anmen Square 天安门广场
Jay Chou 周杰伦
Jay Chou is handsome. He is my favourite actor.
arrow 箭 bow 弓
The Trojan War