1、26.3 实际问题与二次函数实际问题与二次函数(3)解一解一解二解二解三解三探究探究3 图中是抛物线形拱桥，当水面在图中是抛物线形拱桥，当水面在 时，拱顶离水面时，拱顶离水面2m，水面宽水面宽4m，水面下降，水面下降1m时，水面宽度增加了多少？时，水面宽度增加了多少？l继续继续解一解一 以抛物线的顶点为原点，以抛物线的对称轴为以抛物线的顶点为原点，以抛物线的对称轴为 轴，建立平轴，建立平面直角坐标系，如图所示面直角坐标系，如图所示.y可设这条抛物线所表示可设这条抛物线所表示的二次函数的解析式为的二次函数的解析式为:2axy 当拱桥离水面当拱桥离水面2m时时,水面宽水面宽4m即抛物线过点即抛物线
2、过点(2,-2)22a2 5.0a 这条抛物线所表示的二这条抛物线所表示的二次函数为次函数为:2x5.0y 当水面下降当水面下降1m时时,水面的水面的纵坐标为纵坐标为y=-3,这时有这时有:2x5.03 6x m62这这时时水水面面宽宽度度为为当水面下降当水面下降1m时时,水面宽水面宽度增加了度增加了m)462(返回返回解二解二如图所示如图所示,以抛物线和水面的两个交点的连线为以抛物线和水面的两个交点的连线为x轴，以抛物线轴，以抛物线的对称轴为的对称轴为y轴，建立平面直角坐标系轴，建立平面直角坐标系.当拱桥离水面当拱桥离水面2m时时,水面宽水面宽4m即即:抛物线过点抛物线过点(2,0)22a0
3、2 5.0a 这条抛物线所表示的二这条抛物线所表示的二次函数为次函数为:2x5.0y2 当水面下降当水面下降1m时时,水面的水面的纵坐标为纵坐标为y=-1,这时有这时有:2x5.012 6x m62这这时时水水面面宽宽度度为为当水面下降当水面下降1m时时,水面宽水面宽度增加了度增加了m)462(可设这条抛物线所表示可设这条抛物线所表示的二次函数的解析式为的二次函数的解析式为:2axy2 此时此时,抛物线的顶点为抛物线的顶点为(0,2)返回返回解三解三 如图所示如图所示,以抛物线和水面的两个交点的连线为以抛物线和水面的两个交点的连线为x轴，以其中轴，以其中的一个交点的一个交点(如左边的点如左边的
4、点)为原点，建立平面直角坐标系为原点，建立平面直角坐标系.可设这条抛物线所表示可设这条抛物线所表示的二次函数的解析式为的二次函数的解析式为:2)2x(ay2 抛物线过点抛物线过点(0,0)2)2(a02 5.0a 这条抛物线所表示的二这条抛物线所表示的二次函数为次函数为:2)2x(5.0y2 当水面下降当水面下降1m时时,水面的水面的纵坐标为纵坐标为y=-1,这时有这时有:2)2x(5.012 62x,62x21 m62xx12 当水面下降当水面下降1m时时,水面宽水面宽度增加了度增加了m)462(此时此时,抛物线的顶点为抛物线的顶点为(2,2)这时水面的宽度为这时水面的宽度为:返回返回 例例
5、:某工厂大门是一抛物线形的水泥建筑物某工厂大门是一抛物线形的水泥建筑物,大门底部宽大门底部宽AB=4m,顶部顶部C离地面的高度为离地面的高度为4.4m,现有载满货物的汽车现有载满货物的汽车欲通过大门欲通过大门,货物顶部距地面货物顶部距地面2.7m,装货宽度为装货宽度为2.4m.这辆汽这辆汽车能否顺利通过大门车能否顺利通过大门?若能若能,请你通过计算加以说明请你通过计算加以说明;若不能若不能,请简要说明理由请简要说明理由.解：如图，以解：如图，以AB所在的直线为所在的直线为x轴，轴，以以AB的垂直平分线为的垂直平分线为y轴，建立平面轴，建立平面直角坐标系直角坐标系.AB=4A(-2,0)B(2,
6、0)OC=4.4 C(0,4.4)设抛物线所表示的二次函数为设抛物线所表示的二次函数为4.4axy2 抛物线过抛物线过A(-2,0)04.4a4 1.1a 抛物线所表示的二次函数为抛物线所表示的二次函数为4.4x1.1y2 7.2816.24.42.11.1y2.1x2 时，时，当当汽车能顺利经过大门汽车能顺利经过大门.小结小结一般步骤一般步骤:(1).建立适当的直角系建立适当的直角系,并将已知条件转化为点的并将已知条件转化为点的坐标坐标,(2).合理地设出所求的函数的表达式合理地设出所求的函数的表达式,并代入已知并代入已知条件或点的坐标条件或点的坐标,求出关系式求出关系式,(3).利用关系式
7、求解实际问题利用关系式求解实际问题.2.一场篮球赛中一场篮球赛中,球员甲跳起投篮球员甲跳起投篮,如图如图2,已知球在已知球在A处出手处出手时离地面时离地面20/9 m,与篮筐中心与篮筐中心C的水平距离是的水平距离是7m,当球运行的水当球运行的水平距离是平距离是4 m时时,达到最大高度达到最大高度4m（B处）处）,设篮球运行的路线设篮球运行的路线为抛物线为抛物线.篮筐距地面篮筐距地面3m.问此球能否投中问此球能否投中?1.有一辆载有长方体体状集装箱的货车要想通过洞拱横有一辆载有长方体体状集装箱的货车要想通过洞拱横截面为抛物线的隧道，如图截面为抛物线的隧道，如图1，已知沿底部宽，已知沿底部宽AB为
8、为4m，高，高OC为为3.2m；集装箱的宽与车的宽相同都是；集装箱的宽与车的宽相同都是2.4m；集装箱；集装箱顶部离地面顶部离地面2.1m。该车能通过隧道吗？请说明理由。该车能通过隧道吗？请说明理由.(选做选做)此时对方球员乙前来盖帽此时对方球员乙前来盖帽,已知乙跳起后摸到的已知乙跳起后摸到的最大高度为最大高度为3.19m,他如何做才能盖帽成功他如何做才能盖帽成功?作业作业:新课标北师大版课件系列高中英语必修必修2 2Beijing Operathe National TreasureBeijing Opera dates back to the 18th century.It is a co
9、mbination of acting,talking,singing,music,dancing and acrobatics.The costumes are always in bright colour.costumedate backcombinationa national treasurea piercing voiceacrobaticscostumea mixture of two or more thingsthe clothes worn in plays or filmsto have a history ofa group of valuable things,ver
10、y special or important for the countrymovement of ones body using the skills of an acrobata very high and loud voiceTask 1:Listen to an interview about Beijing Opera Listen to an interview about Beijing Opera and answer the following questions.and answer the following questions.1.When did Beijing Op
11、era start?2.What skills do Beijing Opera actors need to have?3.How many main roles are there in Beijing Opera?4.Match the main roles with their names.sheng male roles with brightly painted faces dan female roles jing clown roles chou male roles1.When did Beijing Opera start?It dates back to the late
12、 18th century.2.What skills do Beijing Opera actors need to have?It is a combination of acting,talking,singing,music,dancing and acrobatics.3.How many main roles are there in Beijing Opera?There are four.4.Match the main roles with their names.sheng male roles dan female roles jing male roles with b
13、rightly painted faces chou clown rolesshengdanjingchouBeijing Operahistorymain rolesskills neededTask 2:Listen and use the Strategies to answer Listen and use the Strategies to answer the questions.the questions.1.Where was Beijing Opera performed at the beginning?2.Why does it have very loud music
14、and a piercing singing style?3.Why do performers wear brightly coloured costumes?1.Where was Beijing Opera performed at the beginning?It was performed mostly on open-air stages in markets,streets,teahouses or temple courtyards.2.Why does it have very loud music and a piercing singing style?In order
15、to be heard over the crowds.3.Why do performers wear brightly coloured costumes?In order to be seen by the crowds clearly.Beijing Operahistorymain rolesskills neededcostumesingingQionghua Cantonese Opera Festival1.Read the passage about Cantonese Opera carefully and find out information according to
16、 the diagram.2.Discuss with your group members to find out the similarities and differences between Beijing Opera and Cantonese Opera.Cantonese Operahistorymain rolesskills neededcostumesingingBesides Beijing Opera,there are still other National Treasures in China.They serve as a window of China.And
17、 through this window,foreigners are able to understand Chinese culture better.Besides Beijing Opera,there are still other National Treasures in China.They serve as a window of China.And through this window,foreigners are able to understand Chinese culture better.Beijing Operahistorymain rolesskills neededcostumesingingVarious body movements can represent actionsriding in a carriageriding a horseholding a tassel in his handan army of thousandsfour generals and four soldierswalking with a flag on each side
