九年级数学上册第二十二章二次函数221二次函数的图象和性质2212二次函数y=ax2的图像和性质课件新版新人.ppt

1、22.1.2 二次函数y=ax的图像和性质九年级上册学习目标学习目标 1、正确理解抛物线的有关概念；2、会用描点法画出二次函数y=ax的图象，概括出图象的特点；3、掌握形如y=ax的二次函数图象的性质，并会应用.预习反馈预习反馈1、函数y=x2的图象的开口 ，对称轴 ，顶点是 ；在对称轴的左侧，y随x的增大而 ，在对称轴的右侧，y随x的增大而 ；2、函数y=-x2的图象的开口 ，对称轴 ，顶点是 ；在对称轴的左侧，y随x的增大而 ，在对称轴的右侧，y随x的增大而 ；向上y轴（0,0）减小增大向下y轴（0,0）增大减小消防站也可以很酷，来看荷兰这座像“抛物线”一样的建筑情境引入情境引入x-3-2

2、-10123y=x2 2例1 画出二次函数y=x2的图象.94101941.列表：在y=x2 中自变量x可以是任意实数，列表表示几组对应值：例题解析例题解析24-2-4o369xy2.描点：根据表中x,y的数值在坐标平面中描点（x,y）3.连线：如图，再用平滑曲线顺次连接各点，就得到y=x2 的图象-33o369当取更多个点时，函数y=x2的图象如下：xy 二次函数y=x2的图象形如物体抛射时所经过的路线,我们把它叫做抛物线.这条抛物线关于y轴对称,y轴就是它的对称轴.对称轴与抛物线的交点叫做抛物线的顶点.画出函数 y=-x2 的图象.y24-2-40-3-6-9xx-3-2-10123y=-

3、x2-9-4-1 0-1-4-9 课堂练习课堂练习说说二次函数y=x2的图象有哪些性质，并与同伴交流.xoy=x21.yx2是一条抛物线;2.图象开口向上;3.图象关于y轴对称;4.顶点（0，0）;5.图象有最低点y讨论讨论说说二次函数 y-x2的图象有哪些性质,与同伴交流.oxyy=-x2 1.y-x2是一条抛物线;2.图象开口向下;3.图象关于y轴对称;4.顶点（0，0）;5.图象有最高点1.顶点都在原点;3.当a0时，开口向上；当a0时，开口向下二次函数y=ax2 的图象性质：2.图像关于y轴对称;归纳总结归纳总结观察下列图象，抛物线y=ax2与y=-ax2（a0)的关系是什么？二次项系

4、数互为相反数，开口相反，大小相同，它们关于x轴对称.xyOy=ax2y=-ax2观察观察问题1：观察图形，y随x的变化如何变化？(-2,4)(-1,1)(2,4)(1,1)2yx2yax课堂探究课堂探究对于抛物线 y=ax2（a0)当x0时，y随x取值的增大而增大；当x0时，y随x取值的增大而减小.归纳总结归纳总结(-2,-4)(-1,-1)(2,-4)(1,-1)2yx 2yax 问题2：观察图形，y随x的变化如何变化？课堂探究课堂探究对于抛物线 y=ax2（a0)当x0时，y随x取值的增大而减小；当x0时，a越大，开口越小.练一练：在同一直角坐标系中，画出函数 的图象221,22yx yx

5、x432101234x21.510.500.511.52 -8 -4.5-2 -0.50 -8 -4.5 -2-0.5-8-4.52-0.5084.520.522yx 212yxxyO22246448212yx 22yx 2yx 当a 0a14.说出下列抛物线的开口方向、对称轴和顶点：23xy 23xy231xy 231xy开口方向对称轴顶点向上向下向下向上y轴y轴y轴y轴（0,0）（0,0）（0,0）（0,0）O 5.若抛物线y=ax2（a 0），过点（-1，2）.（1）则a的值是 ；（2）对称轴是 ，开口 .（3）顶点坐标是 ，顶点是抛物线上的最 值.抛物线在x轴的 方（除顶点外）.(4)

6、若A（x1,y1),B(x2,y2)在这条抛物线上，且x1x2 6.已知二次函数y=x2，若xm时，y最小值为0，求实数m的取值范围解：二次函数y=x2，当x=0时，y有最小值，且y最小值=0，当xm时，y最小值=0，m07.已知：如图，直线y3x4与抛物线yx2交于A、B两点，求出A、B两点的坐标，并求出两交点与原点所围成的三角形的面积解：由题意得 解得所以此两函数的交点坐标为A(4，16)和B(1，1)直线y3x4与y轴相交于点C(0，4)，即CO4.SACO CO48，SBOC 412，SABOSACOSBOC10.234,yxyx4,1,16,1,xxyy 或1212课堂小结课堂小结二

7、 次 函 数y=ax2的图象及性质画法描点法以对称轴为中心对称取点图象抛物线轴对称图形性质重 点 关注 4 个方面开口方向及大小对 称 轴顶点坐标增 减 性数学思考：1.画二次函数y=ax的图象时，有哪些地方是你需关注的？2.你是如何理解并熟记抛物线y=ax的性质的？布置作业布置作业再见再见全文结束！再见全文结束！再见o study whether experiences during teen years would influence adult health.So they followed 171 teens,starting when the kids were just 13.Th

8、ey interviewed each one every year for five years，and also spoke to these teens closest friends，who provided additional information about the quality of their friendships.The same 171 people were interviewed again at ages 25,26 and 27.This time,the questions surveyed each persons overall health.When

9、 the researchers analyzed the data,they found a strong connection between a teens behavior and adult health.Teens who had close friends grew up to be the healthier adults.Whether teens held back their feelings or expressed them to close friends also influenced later health.Those who held back their

10、feelings were more likely to be sick as adults.The connection held up even after the scientists accounted for other possible influences on health.Weight，family income and drug use were all examined.So were mental health issues，such as anxiety and depression.And in these people，such other factors did

11、 not explain adult health as well as teen friendships did.Getting along with the crowd may have benefits,says Allen,but there are also drawbacks.Teens who are more independent tend to do better at school and work.And peer pressure may lead some kids to engage in risky behavior,such as smoking,drinking or using drugs.Dealing with it is an ongoing challenge，Allen acknowledges.“Finding the right balance is the key.Teens shouldnt lose heart for not finding this easy.”And,he adds，“Parents need to be understanding about the pressures teens face.”