方程的根和函數(shù)的零點

方程的根和函數(shù)的零點問題1：求下列方程的根(1)(2)(3)方程的根與函數(shù)的零點創(chuàng)設(shè)情境，初步探索，設(shè)問激疑

思考：方程的根與函數(shù)的圖象有什么關(guān)系？方程的根

函數(shù)的圖象與X軸交點

方程函數(shù)函數(shù)的圖象方程的實數(shù)根x1=－1,x2=3x1=x2=1無實數(shù)根函數(shù)的圖象與x軸的交點(－1,0)、(3,0)(1,0)無交點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)的根函數(shù)y=ax2+bx+c(a>0)的簡圖

判別式△=b2－4ac△＞0△=0△＜0函數(shù)的圖象與x軸的交點有兩個相等的實數(shù)根x1=x2沒有實數(shù)根xyx1x20xy0x1xy0(x1,0),(x2,0)(x1,0)沒有交點兩個不相等的實數(shù)根x1、x2對于二次函數(shù)y＝ax2＋bx＋c(a>0)與一元二次方程ax2＋bx＋c＝0(a>0)

，其判別式

＝b2－4ac.方程的根與函數(shù)的零點從特殊到一般

y=0思考：當(dāng)a<0時呢？

對于函數(shù)y=f(x)，我們把使f(x)=0成立的實數(shù)x叫做函數(shù)y=f(x)的零點．方程的根與函數(shù)的零點形成概念,梳理提升函數(shù)零點的定義：2.零點是點還是數(shù)?1.任意函數(shù)都有零點嗎?課堂練習(xí)1：下列函數(shù)有沒有零點，有幾個零點：（1）y=－x2＋3x＋5（2）y=2x(x－2)+3；下列方程有沒有根，有幾個根：（1）－x2＋3x＋5=0（2）2x(x－2)+3=0；這種關(guān)系可以推廣一般情形嗎？方程的根與函數(shù)的零點總結(jié)歸納，知識拓展

對于任意方程f（x）=0與對應(yīng)函數(shù)y=f（x），上述結(jié)論是否成立呢？（1）（2）問題1：此圖象是否能表示函數(shù)？問題2：你能從中分析函數(shù)有哪些零點嗎？-2-123方程的根與函數(shù)的零點等價關(guān)系,梳理提升函數(shù)y=f(x)有零點方程f(x)=0有實數(shù)根函數(shù)y=f(x)的圖象與x軸有交點1.2.

問題探究觀察函數(shù)的圖象①在區(qū)間(a,b)上______(有/無)零點；f(a).f(b)_____0（＜或＞）．②在區(qū)間(b,c)上______(有/無)零點；f(b).f(c)_____0（＜或＞）．③在區(qū)間(c,d)上______(有/無)零點；f(c).f(d)_____0（＜或＞）．-15-4<3<有<有<有<發(fā)現(xiàn)：零點存在性定理討論：（1）從這一結(jié)論中可看出，函數(shù)具備了哪些條件，就可斷言它有零點存在呢？（2）如果函數(shù)具備上述兩個條件時，函數(shù)有多少零點呢？（3）如果把結(jié)論中的條件“圖象連續(xù)不斷”除去不要，又會怎樣呢？（5）若函數(shù)y=f(x)在區(qū)間(a,b)內(nèi)有零點，一定能得出f(a)·f(b)<0的結(jié)論嗎？（6）在什么樣的條件下，就可確定零點的個數(shù)呢，零點的個數(shù)是惟一的呢？

（4）如果把結(jié)論中的條件“f(a)f(b)＜0’’去掉呢？例課堂練習(xí)2：

課堂小結(jié)：

課后作業(yè)：

1、求下列函數(shù)的零點：(1)y=-x2+6x+7；

(2)y=x3-4x。

2、若函數(shù)f(x)=x2-ax-b的兩個零點是2和3，求loga25+b2。１、函數(shù)零點的定義；2、函數(shù)的零點與方程的根的關(guān)系；3、確定函數(shù)的零點的方法。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