1、第2章 一元二次函数、方程和不等式2.3 二次函数与一元二次方程、不等式导问:创设情境,引入主题No.1 Senior Middle School of Siping数学小游戏.enbxNo.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping导问:创设情境,引入主题No.1 Senior Middle School of Siping【问题1】园艺师傅打算在绿地上用栅栏围成一个矩形区域种植花卉,若栅栏的长度是24 m,围成的矩形区域的面积要等于20 m 2,则这个矩形的边长为多少米?No.1 Senior Mi
2、ddle School of Siping导问:创设情境,引入主题No.1 Senior Middle School of Siping【问题1】园艺师傅打算在绿地上用栅栏围成一个矩形区域种植花卉,若栅栏的长度是24 m,围成的矩形区域的面积要等于20 m 2,则这个矩形的边长为多少米?设未知数列方程求解方程No.1 Senior Middle School of Siping导问:创设情境,引入主题No.1 Senior Middle School of Siping【问题1】园艺师傅打算在绿地上用栅栏围成一个矩形区域种植花卉,若栅栏的长度是24 m,围成的矩形区域的面积要等于20 m 2,
3、则这个矩形的边长为多少米?设未知数列方程求解方程No.1 Senior Middle School of Siping导问:创设情境,引入主题No.1 Senior Middle School of Siping【问题1】园艺师傅打算在绿地上用栅栏围成一个矩形区域种植花卉,若栅栏的长度是24 m,围成的矩形区域的面积要等于20 m 2,则这个矩形的边长为多少米?设未知数列方程求解方程No.1 Senior Middle School of Siping导问:创设情境,引入主题No.1 Senior Middle School of Siping【问题1】园艺师傅打算在绿地上用栅栏围成一个矩形区
4、域种植花卉,若栅栏的长度是24 m,围成的矩形区域的面积要等于20 m 2,则这个矩形的边长为多少米?设未知数列方程求解方程No.1 Senior Middle School of Siping导问:创设情境,引入主题No.1 Senior Middle School of Siping【问题1】园艺师傅打算在绿地上用栅栏围成一个矩形区域种植花卉,若栅栏的长度是24 m,围成的矩形区域的面积要等于20 m 2,则这个矩形的边长为多少米?设未知数列方程求解方程No.1 Senior Middle School of Siping导问:创设情境,引入主题No.1 Senior Middle Sch
5、ool of SipingNo.1 Senior Middle School of Siping导问:创设情境,引入主题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping导问:创设情境,引入主题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping导问:创设情境,引入主题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping零点是点吗?
6、导问:创设情境,引入主题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping注意:零点不是点,是交点的横坐标,是数零点是点吗?导问:创设情境,引入主题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping零点是点吗?注意:零点不是点,是交点的横坐标,是数导问:创设情境,引入主题No.1 Senior Middle School of Siping【问题1】园艺师傅打算在绿地上用栅栏围成一个矩形区域种植花卉,若栅栏的长度是2
7、4 m,围成的矩形区域的面积要等于20 m 2,则这个矩形的边长为多少米?设未知数列方程求解方程No.1 Senior Middle School of Siping深问:步步设疑,激发思考No.1 Senior Middle School of Siping【问题2】园艺师傅打算在绿地上用栅栏围成一个矩形区域种植花卉,若栅栏的长度是24 m,围成的矩形区域的面积要大于20 m 2,则这个矩形的边长为多少米?设未知数列方程求解方程No.1 Senior Middle School of Siping深问:步步设疑,激发思考No.1 Senior Middle School of Siping【
8、问题2】园艺师傅打算在绿地上用栅栏围成一个矩形区域种植花卉,若栅栏的长度是24 m,围成的矩形区域的面积要大于20 m 2,则这个矩形的边长为多少米?设未知数列方程求解方程No.1 Senior Middle School of Siping(1)求得(1)的解集,我们就能得出问题的答案。深问:步步设疑,激发思考No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping一般地,我们把只含有一个未知数,并且未知数的最高次项是2的不等式,称为一元二次不等式。它的一般形式是:深问:步步设疑,激发思考No.1 Senio
9、r Middle School of SipingNo.1 Senior Middle School of Siping一般地,我们把只含有一个未知数,并且未知数的最高次项是2的不等式,称为一元二次不等式。它的一般形式是:深问:步步设疑,激发思考No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping一般地,我们把只含有一个未知数,并且未知数的最高次项是2的不等式,称为一元二次不等式。它的一般形式是:深问:步步设疑,激发思考No.1 Senior Middle School of SipingNo.1 Seni
10、or Middle School of Siping一般地,我们把只含有一个未知数,并且未知数的最高次项是2的不等式,称为一元二次不等式。它的一般形式是:深问:步步设疑,激发思考No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping解问:合作探究,共解问题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping几何解释?解问:合作探究,共解问题No.1 Senior Middle School of SipingNo.1 Se
11、nior Middle School of Siping几何解释?解问:合作探究,共解问题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping几何解释?三者紧密相关解问:合作探究,共解问题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping【问题3】能否类比一元一次不等式的求解方法,从二次函数的观点来看一元二次不等式,进而得到一元二次不等式的求解方法呢?解问:合作探究,共解问题No.1 Senior Middle Sch
12、ool of SipingNo.1 Senior Middle School of Siping解问:合作探究,共解问题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping解问:合作探究,共解问题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping问题4:你可以将上述方法推广到求一般的一元二次不等式的解集吗?一般的一元二次方程,一元二次不等式与相应的函数,这三个“二次”之间具有什么关系呢?解问:合作探究,共解问题No.1
13、 Senior Middle School of SipingNo.1 Senior Middle School of Siping问题4:你可以将上述方法推广到求一般的一元二次不等式的解集吗?一般的一元二次方程,一元二次不等式与相应的函数,这三个“二次”之间具有什么关系呢?解问:合作探究,共解问题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping解问:合作探究,共解问题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Sipi
14、ng解问:合作探究,共解问题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping解问:合作探究,共解问题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping解问:合作探究,共解问题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping解问:合作探究,共解问题No.1 Senior Middle School of SipingNo.1
15、Senior Middle School of Siping解问:合作探究,共解问题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping解问:合作探究,共解问题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping解问:合作探究,共解问题No.1 Senior Middle School of Siping No.1 Senior Middle School of Siping解问:合作探究,共解问题No.1 Senior
16、 Middle School of Siping No.1 Senior Middle School of Siping解问:合作探究,共解问题No.1 Senior Middle School of Siping没有实数根 No.1 Senior Middle School of Siping解问:合作探究,共解问题No.1 Senior Middle School of Siping没有实数根R No.1 Senior Middle School of Siping解问:合作探究,共解问题No.1 Senior Middle School of Siping没有实数根R No.1 Seni
17、or Middle School of Siping解问:合作探究,共解问题No.1 Senior Middle School of Siping有人说:当0时,表中的x1,x2有三重身份,你能说出是哪三重身份吗?No.1 Senior Middle School of Siping解问:合作探究,共解问题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping问题4:你可以将上述方法推广到求一般的一元二次不等式的解集吗?一般的一元二次方程,一元二次不等式与相应的函数,这三个“二次”之间具有什么关系呢?解问:合
18、作探究,共解问题No.1 Senior Middle School of Siping没有实数根R No.1 Senior Middle School of Siping解问:合作探究,共解问题No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping解问:合作探究,共解问题No.1 Senior Middle School of Siping数缺形时少直观,形少数时难入微;数形结合百般好,隔离分家万事休。No.1 Senior Middle School of Siping华罗庚为中国数学发展作出了巨大贡献,被
19、誉为“中国现代数学之父”。解问:合作探究,共解问题No.1 Senior Middle School of Siping数缺形时少直观,形少数时难入微;数形结合百般好,隔离分家万事休。No.1 Senior Middle School of Siping华罗庚为中国数学发展作出了巨大贡献,被誉为“中国现代数学之父”。解问:合作探究,共解问题No.1 Senior Middle School of Siping【小试牛刀】思辨解析(正确的打“”,错误的打“”)(1)mx25x0,则一元二次不等式ax210无解.()(3)若一元二次方程ax2bxc0的两根为x1,x2(x1x2),则一元二次不等式
20、ax2bxc0的解集为x|x1x0的解集为R.()新问:点拨归纳,提升思维No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping新问:点拨归纳,提升思维No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping新问:点拨归纳,提升思维No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping新问:点拨归纳,提升思维No.1 Senior Middl
21、e School of SipingNo.1 Senior Middle School of Siping新问:点拨归纳,提升思维No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping新问:点拨归纳,提升思维No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping新问:点拨归纳,提升思维No.1 Senior Middle School of SipingNo.1 Senior Middle School of Siping思
22、考:你能否总结一下求解一元二次不等式的步骤是什么?新问:点拨归纳,提升思维No.1 Senior Middle School of Siping例2 已知关于x的不等式x2axb0的解集为x|1x2,求a、b的值新问:点拨归纳,提升思维No.1 Senior Middle School of Siping例2 已知关于x的不等式x2axb0的解集为x|1x2,求a、b的值解:x2axb0的解集为x|1x2,1,2是x2axb0的两根由韦达定理有b12,a12,得b2,a3新问:点拨归纳,提升思维No.1 Senior Middle School of Siping例3 解关于x的不等式x2ax
23、2a20(aR)新问:点拨归纳,提升思维No.1 Senior Middle School of Siping例3 解关于x的不等式x2ax2a20(aR)解:原不等式转化为(x2a)(xa)-a,即a0时,不等式的解集为x|-ax2a;当2a-a,即a0时,原不等式化为x20,无解;当2a-a,即a0时,不等式的解集为x|2ax0时,原不等式的解集为x|-ax2a;当a0时,原不等式的解集为;当a0时,原不等式的解集为x|2ax-a新问:点拨归纳,提升思维No.1 Senior Middle School of Siping练习3 解关于x的不等式(aR):x2(aa2)xa30.新问:点拨
24、归纳,提升思维No.1 Senior Middle School of Siping练习3 解关于x的不等式(aR):x2(aa2)xa30.解:将不等式x2(aa2)xa30变形为(xa)(xa2)0.当a0时,有aa2,所以不等式的解集为x|xa或xa2;当a0时,aa20,所以不等式的解集为x|xR,且x0;当0a1时,有aa2,所以不等式的解集为x|xa2或xa;当a1时,aa21,所以不等式的解集为x|xR,且x1;当a1时,有aa2,所以不等式的解集为x|xa或xa2.新问:点拨归纳,提升思维No.1 Senior Middle School of Siping【课堂小结】新问:点
25、拨归纳,提升思维No.1 Senior Middle School of Siping【课堂小结】一元二次方程一元二次方程根零点二次函数二次函数新问:点拨归纳,提升思维No.1 Senior Middle School of Siping【课堂小结】定义定义一元二次方程一元二次方程根零点二次函数二次函数新问:点拨归纳,提升思维No.1 Senior Middle School of Siping【课堂小结】定义定义求解求解方法方法一元二次方程一元二次方程根零点一元一次不等式一元一次不等式类比二次函数二次函数新问:点拨归纳,提升思维No.1 Senior Middle School of Sip
26、ing【课堂小结】定义定义一元二次方程一元二次方程根零点一元一次不等式一元一次不等式类比二次函数二次函数化标准式化标准式(变形,系数为正,右侧为0)求判别式、求实根求判别式、求实根画图像画图像写解集写解集求解求解方法方法新问:点拨归纳,提升思维No.1 Senior Middle School of Siping【课堂小结】定义定义一元二次方程一元二次方程根零点一元一次不等式一元一次不等式类比二次函数二次函数化标准式化标准式(变形,系数为正,右侧为0)求判别式、求实根求判别式、求实根画图像画图像写解集写解集求解求解方法方法数形结合新问:点拨归纳,提升思维No.1 Senior Middle S
27、chool of Siping【课堂小结】定义定义一元二次方程一元二次方程根应用应用零点一元一次不等式一元一次不等式类比二次函数二次函数化标准式化标准式(变形,系数为正,右侧为0)求判别式、求实根求判别式、求实根画图像画图像写解集写解集求解求解方法方法数形结合新问:点拨归纳,提升思维No.1 Senior Middle School of Siping【课后作业】必做:教材55页习题2.3 1,2,3,4,5选做:用函数理解方程和不等式是数学的基本思想方法,其中函数的图像、零图像与x轴的关系等是关键要素,你能以函数观点看一元二次方程,一元二次不等式为例,谈谈体会吗?(300字以内)新问:点拨归纳,提升思维感谢聆听,敬请批评指正!授课教师:王博艺