方程的根和函数的零点

方程的根和函数的零点问题1：求下列方程的根(1)(2)(3)方程的根与函数的零点创设情境，初步探索，设问激疑

思考：方程的根与函数的图象有什么关系？方程的根

函数的图象与X轴交点

方程函数函数的图象方程的实数根x1=－1,x2=3x1=x2=1无实数根函数的图象与x轴的交点(－1,0)、(3,0)(1,0)无交点xy0－132112－1－2－3－4..........xy0－132112543.....yx0－12112x2－2x+1=0x2－2x+3=0y=x2－2x－3y=x2－2x+1x2－2x－3=0y=x2－2x+3方程ax2+bx+c=0(a>0)的根函数y=ax2+bx+c(a>0)的简图

判别式△=b2－4ac△＞0△=0△＜0函数的图象与x轴的交点有两个相等的实数根x1=x2没有实数根xyx1x20xy0x1xy0(x1,0),(x2,0)(x1,0)没有交点两个不相等的实数根x1、x2对于二次函数y＝ax2＋bx＋c(a>0)与一元二次方程ax2＋bx＋c＝0(a>0)

，其判别式

＝b2－4ac.方程的根与函数的零点从特殊到一般

y=0思考：当a<0时呢？

对于函数y=f(x)，我们把使f(x)=0成立的实数x叫做函数y=f(x)的零点．方程的根与函数的零点形成概念,梳理提升函数零点的定义：2.零点是点还是数?1.任意函数都有零点吗?课堂练习1：下列函数有没有零点，有几个零点：（1）y=－x2＋3x＋5（2）y=2x(x－2)+3；下列方程有没有根，有几个根：（1）－x2＋3x＋5=0（2）2x(x－2)+3=0；这种关系可以推广一般情形吗？方程的根与函数的零点总结归纳，知识拓展

对于任意方程f（x）=0与对应函数y=f（x），上述结论是否成立呢？（1）（2）问题1：此图象是否能表示函数？问题2：你能从中分析函数有哪些零点吗？-2-123方程的根与函数的零点等价关系,梳理提升函数y=f(x)有零点方程f(x)=0有实数根函数y=f(x)的图象与x轴有交点1.2.

问题探究观察函数的图象①在区间(a,b)上______(有/无)零点；f(a).f(b)_____0（＜或＞）．②在区间(b,c)上______(有/无)零点；f(b).f(c)_____0（＜或＞）．③在区间(c,d)上______(有/无)零点；f(c).f(d)_____0（＜或＞）．-15-4<3<有<有<有<发现：零点存在性定理讨论：（1）从这一结论中可看出，函数具备了哪些条件，就可断言它有零点存在呢？（2）如果函数具备上述两个条件时，函数有多少零点呢？（3）如果把结论中的条件“图象连续不断”除去不要，又会怎样呢？（5）若函数y=f(x)在区间(a,b)内有零点，一定能得出f(a)·f(b)<0的结论吗？（6）在什么样的条件下，就可确定零点的个数呢，零点的个数是惟一的呢？

（4）如果把结论中的条件“f(a)f(b)＜0’’去掉呢？例课堂练习2：

课堂小结：

课后作业：

1、求下列函数的零点：(1)y=-x2+6x+7；

(2)y=x3-4x。

2、若函数f(x)=x2-ax-b的两个零点是2和3，求loga25+b2。１、函数零点的定义；2、函数的零点与方程的根的关系；3、确定函数的零点的方法。3jtEOY-9jtDOY-8itDNX-8isCNX)7isCMX)7hrCMW(7hrBLW(6grBLV*6gqALV*5gqAKU*5fpAKU&4fpzJU&4epzJT%4eoyJT%3doyIS%3dnyIS$2dnxHS$2cmxHR!2cmwHR!1bmwGQ!1blvGQ#0blvFQ#0akvFPZ0akuEPZ+9kuEOY+9jtEOY-9jtDNY-8itDNX)8isCNX)7isCMW)7hrCMW(6hrBLW(6grBLV*6gqALV*5fqAKU*5fpAKU&4fpzJU&4eozJT%4eoyIT%3doyIS%3dnxIS$2dnxHR$2cmxHR!2cmwGR!1bmwGQ#1blvGQ#0blvFP#0akvFPZ+akuEPZ+9kuEOY+9jtEOY-8jtDNY-8itDNX)8isCNX)7hsCMW)7hrBMW(6hrBLW(6gqBLV*6gqAKV*5fqAKU*5fpzKU&4fpzJT&4eozJT%4eoyIT%3doyIS$3dnxIS$2dnxHR$2cmxHR!1cmwGR!1bmwGQ#1blvGQ#0alvFP#0akuFPZ+akuEPZ+9juEOY+9jtDOY-8jtDNY-8isDNX)8isCMX)7hsCMW)7hrBMW(6hrBLV(6gqBLV*6gqAKV*5fqAKU&5fpzKU&4fpzJT&4eozJT%3eoyIT%3dnyIS$3dnxIS$2cnxHR$2cmwHR!1cmwGR!1blwGQ#1blvFQ#0alvFP#0akuFPZ+akuEOZ+9juEOY+9jtDOY-8jtDNX-8isDNX)8isCMX)7hsCMW(7hrBMW(6grBLV(6gqBLV*5gqAKV*5fpAKU&5fpzKU&4epzJT&4eoyJT%3eoyIT%3dnyIS$3dnxHS$2cnxHR$2cmwHR!1cmwGQ!1blwGQ#1blvFQ#0alvFPZ0akuFPZ+9kuEOZ+9juEOY-9jtDOY-8itDNX-8isDNX)7isCMX)7hrCMW(7hrBMW(6grBLV(6gqALV*5gqAKV*5fpAKU&5fpzJU&4epzJT&4eoyJT%3eoyIS%3dnyIS$2dnxHS$2cnxHR!2cmwHR!1bmwGQ!1blwGQ#0blvFQ#0akvFPZ0akuFPZ+9kuEOZ+9jtEOY-9jtDOY-8itDNX-8isCNX)7isCMX)7hrCMW(7hrBLW(6grBLV*6gqALV*5gqAKU*5fpAKU&4fpzJU&4epzJT%4eoyJT%3doyIS%3dnyIS$2dnxHS$2cmxHR!2cmwHR!1bmwGQ!1blvGQ#0blvFQ#0akvFPZ0akuEPZ+9kuEOY+9jtEOY-9jtDNY-8itDNX)8isCNX)7isCMW)7hrCMW(6hrBLW(6grBLV*6gqALV*5fqAKU*5fpAKU&4fpzJU&4eozJT%4eoyIT%3doyIS%3dnxIS$2dnxHR$2cmxHR!2cmwGR!1bmwGQ#1blvGQ#0blvFP#0akvFPZ+akuEPZ+9kuEOY+9jtEOY-8jtDNY-8itDNX)8isCNX)7hsCMW)7hrBMW(6hrBLW(6gqBLV*6gqAKV*5fqAKU*5fpzKU&4fpzJT&4eozJT%4eoyIT%3doyIS$3dnxIS$2dnxHR$2cmxHR!1cmwGR!1bmwGQ#1blvGQ#0alvFP#0akuFPZ+akuEPZ+9juEOY+9jtDOY-8jtDNY-8isDNX)8isCMX)7hsCMW)7hrBMW(6hrBLV(6gqBLV*6gqAKV*5fqAKU&5fpzKU&4fpzJT&4eozJT%3eoyIT%3dnyIS$3dnxIS$2cnxHR$2cmwHR!1cmwGR!1blwGQ#1blvFQ#0alvFP#0akuFPZ+akuEOZ+9juEOY+9jtDOY-8jtDNX-8isDNX)8isCMX)7hsCMW(7hrBMW(6grBLV(6gqBLV*5gqAKV*5fpAKU&5fpzKU&4e9juEOY+9jtEOY-8jtDNY-8isDNX)8isCNX)7hsCMW)7hrBMW(6hrBLW(6gqBLV*6gqAKV*5fqAKU&5fpzKU&4fpzJT&4eozJT%3eoyIT%3doyIS$3dnxIS$2cnxHR$2cmxHR!1cmwGR!1blwGQ#1blvGQ#0alvFP#0akuFPZ+akuEPZ+9juEOY+9jtDOY-8jtDNX-8isDNX)8isCMX)7hsCMW(7hrBMW(6hrBLV(6gqBLV*5gqAKV*5fqAKU&5fpzKU&4epzJT&4eozJT%3eoyIT%3dnyIS$3dnxIS$2cnxHR$2cmwHR!1cmwGQ!1blwGQ#1blvFQ#0alvFPZ0akuFPZ+akuEOZ+9juEOY-9jtDOY-8jtDNX-8isDNX)7isCMX)7hsCMW(7hrBMW(6grBLV(6gqBLV*5gqAKV*5fpAKU&5fpzJU&4epzJT&4eoyJT%3eoyIS%3dnyIS$3dnxHS$2cnxHR!2cmwHR!1cmwGQ!1blwGQ#0blvFQ#0alvFPZ0akuFPZ+9kuEOZ+9juEOY-9jtDOY-8itDNX-8isCNX)7isCMX)7hrCMW(7hrBLW(6grBLV(6gqALV*5gqAKU*5fpAKU&5fpzJU&4epzJT%4eoyJT%3eoyIS%3dnyIS$2dnxHS$2cnxHR!2cmwHR!1bmwGQ!1blvGQ#0blvFQ#0akvFPZ0akuEPZ+9kuEOZ+9jtEOY-9jtDNY-8itDNX-8isCNX)7isCMW)7hrCMW(7hrBLW(6grBLV*6gqALV*5fqAKU*5fpAKU&4fpzJU&4eozJT%4eoyJT%3doyIS%3dnxIS$2dnxHS$2cmxHR!2cmwGR!1bmwGQ!1blvGQ#0blvFP#0akvFPZ0akuEPZ+9kuEOY+9jtEOY-8jtDNY-8itDNX)8isCNX)7hsCMW)7hrCMW(6hrBLW(6gqBLV*6gqALV*5fqAKU*5fpzKU&4fpzJU&4eozJT%4eoyIT%3doyIS%3dnxIS$2dnxHR$2cmxHR!1cmwGR!1bmwGQ#1blvGQ#0alvFP#0akvFPZ+akuEPZ+9juEOY+9jtEOY-8jtDNY-8isDNX)8isCNX)7hsCMW)7hrBMW(6hrBLW(6gqBLV*6gqAKV*5fqAKU&5fpzKU&4fpzJT&4eozJT%3eoyIT%3doyIS$3dnxIS$2cnxHR$2cmxHR!1cmwGR!1blwGQ#1blvGQ#0a1blwGQ#0blvFQ#0alvFPZ0akuFPZ+9kuEOZ+9jtEOY-9jtDOY-8itDNX-8isCNX)7isCMX)7hrCMW(7hrBLW(6grBLV(6gqALV*5gqAKU*5fpAKU&5fpzJU&4epzJT%4eoyJT%3eoyIS%3dnyIS$2dnxHS$2cmxHR!2cmwHR!1bmwGQ!1blvGQ#0blvFQ#0akvFPZ0akuEPZ+9kuEOZ+9jtEOY-9jtDNY-8itDNX-8isCNX)7isCMW)7hrCMW(6hrBLW(6grBLV*6gqALV*5fqAKU*5fpAKU&4fpzJU&4eozJT%4eoyJT%3doyIS%3dnxIS$2dnxHS$2cmxHR!2cmwGR!1bmwGQ!1blvGQ#0blvFP#0akvFPZ+akuEPZ+9kuEOY+9jtEOY-8jtDNY-8itDNX)8isCNX)7hsCMW)7hrCMW(6hrBLW(6gqBLV*6gqALV*5fqAKU*5fpzKU&4fpzJU&4eozJT%4eoyIT%3doyIS$3dnxIS$2dnxHR$2cmxHR!1cmwGR!1bmwGQ#1blvGQ#0alvFP#0akvFPZ+akuEPZ+9juEOY+9jtEOY-8jtDNY-8isDNX)8isCNX)7hsCMW)7hrBMW(6hrBLV(6gqBLV*6gqAKV*5fqAKU&5fpzKU&4fpzJT&4eozJT%3eoyIT%3doyIS$3dnxIS$2cnxHR$2cmxHR!1cmwGR!1blwGQ#1blvGQ#0alvFP#0akuFPZ+akuEOZ+9juEOY+9jtDOY-8jtDNX-8isDNX)8isCMX)7hsCMW(7hrBMW(6hrBLV(6gqBLV*5gqAKV*5fqAKU&5fpzKU&4epzJT&4eozJT%3eoyIT%3dnyIS$3dnxHS$2cnxHR$2cmwHR!1cmwGQ!1blwGQ#1blvFQ#0alvFPZ0akuFPZ+akuEOZ+9juEOY-9jtDOY-8jtDNX-8isDNX)7isCMX)7hsCMW(7hrBMW(6grBLV(6gqALV*5gqAKV*5fpAKU&5fpzJU&4epzJT&4eoyJT%3eoyIS%3dnyIS$3dnxHS$2cnxHR!2cmwHR!1cmwGQ!1blwGQ#0blvFQ#0alvFPZ0akuFPZ+9kuEOZ+9jtEOY-9jtDOY-8itDNX-8isCNX)7isCtDNX)8isCNX)7hsCMW)7hrCMW(6hrBLW(6gqBLV*6gqALV*5fqAKU*5fpzKU&4fpzJT&4eozJT%4eoyIT%3doyIS$3dnxIS$2dnxHR$2cmxHR!1cmwGR!1bmwGQ#1blvGQ#0alvFP#0akvFPZ