第一篇：函數(shù)與方程教案

第四章：函數(shù)應(yīng)用

§1：函數(shù)與方程

教學(xué)分析:課本選取探究具體的一元二次方程的根與其對(duì)應(yīng)二次函數(shù)的圖像與x軸交點(diǎn)的橫坐標(biāo)之間的關(guān)系作為本節(jié)的入口。其意圖是讓學(xué)生從熟悉的環(huán)境中發(fā)現(xiàn)新知識(shí)，使新知識(shí)與原有知識(shí)形成聯(lián)系。教學(xué)目標(biāo)：

1、讓學(xué)生明確“方程的根”與“函數(shù)的零點(diǎn)”的密切聯(lián)系，學(xué)會(huì)結(jié)合函數(shù)圖像性質(zhì)判斷方程根的個(gè)數(shù)，學(xué)會(huì)用多種方法求方程的根和函數(shù)的零點(diǎn)。

2、通過(guò)本節(jié)學(xué)習(xí)讓學(xué)生掌握“由特殊到一般”的認(rèn)識(shí)規(guī)律，在今后學(xué)習(xí)中利用這一規(guī)律探索更多的未知世界。重點(diǎn)難點(diǎn)：根據(jù)二次函數(shù)圖像與x軸的交點(diǎn)個(gè)數(shù)判斷一元二次方程的根的個(gè)數(shù)；函數(shù)零點(diǎn)的概念。復(fù)習(xí)引入：

同學(xué)們好，今天我們來(lái)進(jìn)行第四章函數(shù)應(yīng)用的學(xué)習(xí)，這一節(jié)課我們先來(lái)學(xué)習(xí)第一節(jié)函數(shù)與方程。在講新課之前，我們已經(jīng)學(xué)習(xí)過(guò)一元一次方程、一元二次方程，并會(huì)對(duì)它們進(jìn)行求解?，F(xiàn)在來(lái)看幾個(gè)方程：①ax+b=0(a?0)這是一個(gè)一元一次方程，我們能很容易求出方程的解是x=－.②ax2+bx+c=0(a?0)這是一個(gè)一元二次方程，在對(duì)一ab元二次方程求解時(shí)我們會(huì)先用判別式△=b2－4ac來(lái)判斷方程是否有實(shí)解。當(dāng)△＞0時(shí)，一元二次方程有兩個(gè)不相等的實(shí)數(shù)根，x1≠x2;當(dāng)△=0時(shí)，一元二次方程有兩個(gè)相等的實(shí)數(shù)根，x1=x2;當(dāng)△＜0時(shí)，一元二次方程沒(méi)有實(shí)數(shù)根。當(dāng)方程有實(shí)數(shù)根時(shí)，我們可以通過(guò)求根公式求出一元二次方程的根：x=

?b?b?4ac2a2。③x5+4x3+3x2+2x+1=0

函數(shù)的零點(diǎn)。

說(shuō)明：①零點(diǎn)是所在函數(shù)圖像與x軸交點(diǎn)的橫坐標(biāo)。

②零點(diǎn)是一個(gè)實(shí)數(shù)，并不是一個(gè)點(diǎn)。③函數(shù)的零點(diǎn)就是相應(yīng)方程的根。

④函數(shù)零點(diǎn)的個(gè)數(shù)與相應(yīng)方程的根的個(gè)數(shù)相等。

學(xué)習(xí)過(guò)零點(diǎn)概念及以上4點(diǎn)說(shuō)明，我們已經(jīng)學(xué)會(huì)判斷零點(diǎn)：要求函數(shù)的零點(diǎn)就要看函數(shù)圖像與x軸是否有交點(diǎn)，也即相應(yīng)方程是否有實(shí)根。因此得到判斷零點(diǎn)的方法。

2． 判斷零點(diǎn)的方法：方程f(x)=0有實(shí)根?函數(shù)y=f(x)的圖像與x軸有交點(diǎn)?函數(shù)y=f(x)有零點(diǎn)?？傻贸觯悍匠蘤(x)=0的實(shí)根與函數(shù)y=f(x)的零點(diǎn)是一一對(duì)應(yīng)的。

那如果所給的函數(shù)的圖像不易畫(huà)出，又不能求出其對(duì)應(yīng)方程的根時(shí)，我們?cè)鯓优袛嗪瘮?shù)有沒(méi)有零點(diǎn)呢？

觀(guān)察例1中第一個(gè)方程的對(duì)應(yīng)圖像：f(x)= x2-2x-3 從圖像上看，我們知道函數(shù)f(x)= x2-2x-3有兩個(gè)零點(diǎn)：-1,3.而能找到區(qū)間[-2,0]使零點(diǎn)-1在[-2,0]內(nèi)，區(qū)間[2,4]使零點(diǎn)3在[2,4]內(nèi)。且有f(-2)=5＞0,f(0)=-3＜0, f(-2)×f(0)＜0;f(2)=-3＜0, f(4)=5＞0, f(2)×f(4)＜0.可以發(fā)現(xiàn)f(-2)×f(0)＜0，函數(shù)f(x)= x2-2x-3在區(qū)間（-2,0）內(nèi)有零點(diǎn)-1是方程x2-2x-3=0的一個(gè)根；同樣地，f(2)×f(4)＜0，函數(shù)f(x)= x2-2x-3在區(qū)間（2,4）內(nèi)有零點(diǎn)3是方程x2-2x-3=0的另一個(gè)根。因此可以得到以下結(jié)論：

3.零點(diǎn)存在性定理： 若函數(shù)y=f(x)在閉區(qū)間[a,b]的圖像是連續(xù)曲

5，一個(gè)小于2。

分析：轉(zhuǎn)化判斷函數(shù)f(x)=（x-2）（x-5）-1在區(qū)間（-∞，2）和(5, +∞)內(nèi)各有一個(gè)零點(diǎn)。

解：考慮函數(shù)f(x)=（x-2）（x-5）-1，有f(2)=（2-2）（2-5）-1=-1＜0，f(5)=（5-2）（5-5）-1=-1＜0，又因?yàn)閒(x)的圖像是開(kāi)口向上的拋物線(xiàn)，在（-∞，2）內(nèi)存在一點(diǎn)a，使f(a)＞0；在(5, +∞)內(nèi)存在一點(diǎn)b，使f(b)＞0，所以?huà)佄锞€(xiàn)與橫軸在（a，2）內(nèi)有一個(gè)交點(diǎn)，在(5, b)內(nèi)也有一個(gè)交點(diǎn)，而該交點(diǎn)即是方程的解。所以方程（x-2）（x-5）=1有兩個(gè)相異的實(shí)數(shù)解，且一個(gè)大于5，一個(gè)小于2。

四、零點(diǎn)存在性定理說(shuō)：“若f(a)×f(b)＜0，則在區(qū)間（a,b）內(nèi)，函數(shù)y=f(x)至少有一個(gè)零點(diǎn)，即相應(yīng)的方程f(x)=0在區(qū)間（a,b）內(nèi)至少有一個(gè)實(shí)數(shù)解”，它只指出了方程f(x)=0實(shí)數(shù)解的存在，并不能判斷具體有多少個(gè)實(shí)數(shù)解。那改為f(a)×f(b)＞0時(shí)，問(wèn)題：如果函數(shù)y=f(x)在區(qū)間[a,b]上的圖像是連續(xù)不斷的一條曲線(xiàn)，并且f(a)×f(b)＞0，那么函數(shù)y=f(x)在區(qū)間（a,b）內(nèi)是否有零點(diǎn)?可能有幾個(gè)零點(diǎn)？

解：零點(diǎn)個(gè)數(shù)可以是任意自然數(shù)?？捎懻撛趨^(qū)間[-3,3]上函數(shù)零點(diǎn)個(gè)數(shù)，來(lái)畫(huà)圖進(jìn)行觀(guān)察。

第二篇：函數(shù)與方程教案

函數(shù)與方程教案

27.3實(shí)踐與探索(第二課時(shí))二次函數(shù)與一元二次方程的關(guān)系 晉城四中 李前進(jìn) 【教學(xué)目標(biāo)】

1、知識(shí)與技能:(1)體會(huì)函數(shù)與方程之間的聯(lián)系，初步體會(huì)利用函數(shù)圖象研究方程問(wèn)題的方法;(2)理解二次函數(shù)圖象與x軸(橫軸)交點(diǎn)的個(gè)數(shù)與一元二次方程的根的個(gè)數(shù)之

間的關(guān)系，理解方程有兩個(gè)不等的實(shí)根、兩個(gè)相等的實(shí)根和沒(méi)有實(shí)根的函數(shù) 圖象特征;22(3)理解一元二次方程ax+bx+c=0的根就是二次函數(shù)與y=ax+bx+c圖象與x軸交

點(diǎn)的橫坐標(biāo)。

2、過(guò)程與方法:(1)由一次函數(shù)與一元一次方程根的聯(lián)系類(lèi)比探求二次函數(shù)與一元二次方程之間 的聯(lián)系;(2)經(jīng)歷類(lèi)比、觀(guān)察、發(fā)現(xiàn)、歸納的探索過(guò)程，體會(huì)函數(shù)與方程相互轉(zhuǎn)化的數(shù)學(xué)

思想和數(shù)形結(jié)合的數(shù)學(xué)思想。

3、情感、態(tài)度與價(jià)值觀(guān): 培養(yǎng)學(xué)生類(lèi)比與猜想、不完全歸納、認(rèn)識(shí)到事物之間的聯(lián)系與轉(zhuǎn)化、體驗(yàn) 探究的樂(lè)趣和學(xué)會(huì)用辨證的觀(guān)點(diǎn)看問(wèn)題的思維品質(zhì)。【重點(diǎn)與難點(diǎn)】

重點(diǎn):經(jīng)歷“類(lèi)比--觀(guān)察--發(fā)現(xiàn)--歸納”而得出二次函數(shù)與一元二次方程的關(guān)系的探

索過(guò)程。

難點(diǎn):準(zhǔn)確理解二次函數(shù)與一元二次方程的關(guān)系。【教法與學(xué)法】

教法:采用“發(fā)現(xiàn)式學(xué)習(xí)”的方式，注重“最近發(fā)展區(qū)”，尋根問(wèn)源，以舊知識(shí)為

基礎(chǔ)創(chuàng)設(shè)問(wèn)題情境，引導(dǎo)學(xué)生經(jīng)歷“類(lèi)比—猜想—觀(guān)察—發(fā)現(xiàn)—?dú)w納—應(yīng)用” 的探究過(guò)程。學(xué)法:探究式學(xué)習(xí)。

appearance of the weld appearance quality technical requirements of the project must not have a molten metal stream does not melt the base metal to weld, weld seam and heat-affected zone surface must not have cracks, pores, defects such as crater and ash, surface smoothing, weld and base metal should be evenly smooth transition.Width 2-3 mm from the edge of weld Groove.Surface reinforcement should be less than or equal to 1 + 0.2 times the slope edge width, and should not be greater than 4 mm.Depth of undercut should be less than or equal to 0.5 mm, total length of the welds on both sides undercut not exceed 10% of the weld length, and long continuous should not be greater than 100 mm.Wrong side should be less than or at 0.2T, and should not be greater than 2 mm(wall thickness mm t)incomplete or not allow 7.5 7.5.1 installation quality process standards of the electrical enclosure Cabinet surface is clean, neat, no significant phenomenon of convex, close to nature, close the door.7.5.2 Cabinet Cabinet face paints no paint, returned to rusted, consistent color.7.5.3 uniform indirect gap from top to bottom, slot width <1.5mm 7.5.4 adjacent Cabinet surface roughness is 0.7.5.5 the cabinets firmly fixed, crafts beautiful.7.5.6 Cabinet surface gauge, switch cabinet mark clear, neat, firm paste.7.5.7 Terminal row of neat, is reliable, the appearance is clean and not damaged.7.5.8 cables neat and clean, solid binding, binding process in appearance.7.5.9 the first cable production firm, crafts beautiful, clear signage does not fade.7.5.10 fireproof plugging tight, no cracks and pores.7.6 7.6.1 of the standard electrical wiring quality technology cable a, the multi-core wire bunch arrangement should be parallel to each other, horizontal wire harness or wire should be perpendicular to the longitudinal multi-core wire bunch.The distance between the wire harness and wire harness symmetry, and as close as possible.B-core wiring harness into round, multi-core wire bunch used g wire binding, fastening 【教學(xué)過(guò)程】

一、詩(shī)詞導(dǎo)入

教師投影:我國(guó)著名數(shù)學(xué)家華羅庚曾經(jīng)說(shuō)過(guò):“數(shù)缺形時(shí)少直觀(guān)，形少數(shù) 時(shí)難入微，數(shù)形結(jié)合百般好，隔離分家萬(wàn)事休?！?學(xué)生齊讀)師:數(shù)學(xué)家的寥寥數(shù)語(yǔ)就將數(shù)與形之間的內(nèi)在聯(lián)系表達(dá)的淋漓盡致。今天，我們通過(guò)研究二次函數(shù)中的數(shù)形結(jié)合來(lái)體會(huì)“數(shù)形結(jié)合百般好”的奧妙～ 設(shè)計(jì)思路:從學(xué)生熟悉的小詩(shī)入手，激發(fā)學(xué)生探究學(xué)習(xí)的積極性。

二、溫故知新 y3那些年，我們一起做過(guò)的題: 2(1)解一元一次方程x+1=0;1(2)畫(huà)一次函數(shù)y=x+1的圖象，并指出函數(shù)y=x+1的圖象 x –2–11O 與x軸的交點(diǎn)坐標(biāo)。–1(3)你會(huì)不畫(huà)圖象求函數(shù)y=3x,3與x軸的交點(diǎn)坐標(biāo)嗎, 師生共同總結(jié):一次函數(shù)y,kx，b的圖象與x軸的交點(diǎn)的橫坐標(biāo)就是一元一次方程kx，b,0的根

設(shè)計(jì)思路:這一環(huán)節(jié)讓學(xué)生通過(guò)對(duì)舊知識(shí)的回顧及對(duì)新知識(shí)的思考，梳理舊知識(shí)，起到承上啟下之效，同時(shí)通過(guò)老師的引導(dǎo)，培養(yǎng)學(xué)生的形成解決一類(lèi)問(wèn)題的通用方法的思維品質(zhì)

三、類(lèi)比猜想

22你覺(jué)得一元二次方程ax+bx+c=0的根與二次函數(shù)y=ax+bx+c之間有聯(lián)系嗎，四、問(wèn)題探究

教師分配研究的任務(wù)，然后小組合作完成，教師提問(wèn)，學(xué)生展示研究成果。設(shè)計(jì)思路: 學(xué)生畫(huà)函數(shù)圖象比較慢，分配任務(wù)既可以節(jié)約時(shí)間，又可以使 每個(gè)學(xué)生都有事可做，能夠很好地完成學(xué)習(xí)任務(wù)。

appearance of the weld appearance quality technical requirements of the project must not have a molten metal stream does not melt the base metal to weld, weld seam and heat-affected zone surface must not have cracks, pores, defects such as crater and ash, surface smoothing, weld and base metal should be evenly smooth transition.Width 2-3 mm from the edge of weld Groove.Surface reinforcement should be less than or equal to 1 + 0.2 times the slope edge width, and should not be greater than 4 mm.Depth of undercut should be less than or equal to 0.5 mm, total length of the welds on both sides undercut not exceed 10% of the weld length, and long continuous should not be greater than 100 mm.Wrong side should be less than or at 0.2T, and should not be greater than 2 mm(wall thickness mm t)incomplete or not allow 7.5 7.5.1 installation quality process standards of the electrical enclosure Cabinet surface is clean, neat, no significant phenomenon of convex, close to nature, close the door.7.5.2 Cabinet Cabinet face paints no paint, returned to rusted, consistent color.7.5.3 uniform indirect gap from top to bottom, slot width <1.5mm 7.5.4 adjacent Cabinet surface roughness is 0.7.5.5 the cabinets firmly fixed, crafts beautiful.7.5.6 Cabinet surface gauge, switch cabinet mark clear, neat, firm paste.7.5.7 Terminal row of neat, is reliable, the appearance is clean and not damaged.7.5.8 cables neat and clean, solid binding, binding process in appearance.7.5.9 the first cable production firm, crafts beautiful, clear signage does not fade.7.5.10 fireproof plugging tight, no cracks and pores.7.6 7.6.1 of the standard electrical wiring quality technology cable a, the multi-core wire bunch arrangement should be parallel to each other, horizontal wire harness or wire should be perpendicular to the longitudinal multi-core wire bunch.The distance between the wire harness and wire harness symmetry, and as close as possible.B-core wiring harness into round, multi-core wire bunch used g wire binding, fastening 表格一: 二次函數(shù) 函數(shù)圖象 圖象與x軸方程的根 一元二次 方程 的交點(diǎn)坐 標(biāo) 22 y=x+2x x+2x=0 22y=x-2x+1 x-2x+1=0 22y=x-2x+2-2x+2=0 x

五、歸納結(jié)論

2(1)從“數(shù)”的方面看，當(dāng)二次函數(shù)y=ax+bx+c的函數(shù)值y=_0_ 時(shí)，二次函數(shù) x2-2x+ 2 變?yōu)橐辉畏匠蘟x+bx+c=0,此時(shí)相應(yīng)的_自變量的值即為二次方程 2ax+bx+c=0的_根_;2=0(2)從“形”的方面看，當(dāng)二次函數(shù)的y值為0時(shí)，從圖像看指的是二次函數(shù)圖 像與_x軸_的交點(diǎn)，此時(shí)二次函數(shù)y=ax+bx+c與x軸交點(diǎn)的_橫坐標(biāo)_即為二x2-2x+ 2次方程ax+bx+c=0的_根_。表格二: 2=0 2一元二次方程二次函數(shù)y=ax+bx+c的圖象一元二次方程根的判別式 222b,4ac ax+bx+c=0的根的個(gè)數(shù) 與x軸交點(diǎn)的個(gè)數(shù)

x-2x+ 22=0 b,4ac>0 2 b,4ac=0 2 b,4ac<0 教師和學(xué)生一起總結(jié): 2二次函數(shù)y=ax+bx+c的圖象與x軸的交點(diǎn)有三種情況:有兩個(gè)交點(diǎn)、有一 2個(gè)交點(diǎn)、沒(méi)有交點(diǎn)。當(dāng)二次函數(shù)y=ax+bx+c的圖象與x軸有交點(diǎn)時(shí)，交點(diǎn)的橫 2坐標(biāo)就是當(dāng)y=0時(shí)自變量x的值，即一元二次方程ax+bx+c=0的根。appearance of the weld appearance quality technical requirements of the project must not have a molten metal stream does not melt the base metal to weld, weld seam and heat-affected zone surface must not have cracks, pores, defects such as crater and ash, surface smoothing, weld and base metal should be evenly smooth transition.Width 2-3 mm from the edge of weld Groove.Surface reinforcement should be less than or equal to 1 + 0.2 times the slope edge width, and should not be greater than 4 mm.Depth of undercut should be less than or equal to 0.5 mm, total length of the welds on both sides undercut not exceed 10% of the weld length, and long continuous should not be greater than 100 mm.Wrong side should be less than or at 0.2T, and should not be greater than 2 mm(wall thickness mm t)incomplete or not allow 7.5 7.5.1 installation quality process standards of the electrical enclosure Cabinet surface is clean, neat, no significant phenomenon of convex, close to nature, close the door.7.5.2 Cabinet Cabinet face paints no paint, returned to rusted, consistent color.7.5.3 uniform indirect gap from top to bottom, slot width <1.5mm 7.5.4 adjacent Cabinet surface roughness is 0.7.5.5 the cabinets firmly fixed, crafts beautiful.7.5.6 Cabinet surface gauge, switch cabinet mark clear, neat, firm paste.7.5.7 Terminal row of neat, is reliable, the appearance is clean and not damaged.7.5.8 cables neat and clean, solid binding, binding process in appearance.7.5.9 the first cable production firm, crafts beautiful, clear signage does not fade.7.5.10 fireproof plugging tight, no cracks and pores.7.6 7.6.1 of the standard electrical wiring quality technology cable a, the multi-core wire bunch arrangement should be parallel to each other, horizontal wire harness or wire should be perpendicular to the longitudinal multi-core wire bunch.The distance between the wire harness and wire harness symmetry, and as close as possible.B-core wiring harness into round, multi-core wire bunch used g wire binding, fastening 設(shè)計(jì)思路:通過(guò)教師引導(dǎo)學(xué)生完成表格，使學(xué)生對(duì)命題的內(nèi)涵理解，“學(xué)生對(duì)數(shù)學(xué)命題中各部分符號(hào)的含義能深刻理解，發(fā)現(xiàn)并知道各部分間的內(nèi)在聯(lián)系。”填空使學(xué)生從“形”與“數(shù)”的角度體會(huì)數(shù)形結(jié)合思想，以及方程與函數(shù)互相轉(zhuǎn)化的思想，從而歸納出具一般性的結(jié)論。y22y = x x 6

1六、基礎(chǔ)練習(xí)x–3–2–1123O2–1(1)已知二次函數(shù)y=x-x-6的圖象如圖所示: –2 –3圖象與x軸有2個(gè)交點(diǎn)，交點(diǎn)的橫坐標(biāo) –42 是______,則方程x-x-6=0有__個(gè)根，方程的根是________ 2(2)函數(shù)y= x-5x+6的圖象與x軸有___個(gè)交點(diǎn),其交點(diǎn)坐標(biāo)為_(kāi)________、__________。(3)自命題

每個(gè)小組按照教師的要求，小組內(nèi)通過(guò)討論寫(xiě)出一個(gè)一般式的二次函數(shù)關(guān)系式，用關(guān)系式出一道有關(guān)二次函數(shù)和一元二次方程的簡(jiǎn)單的題，(七個(gè)大組分三種情況布置有目的性的布置，各小組只知道自己小組的任務(wù))。教師通過(guò)在教師內(nèi)觀(guān)察學(xué)生活動(dòng)情況，選兩個(gè)代表性題由其他小組來(lái)做。

設(shè)計(jì)思路:小組活動(dòng)，激發(fā)學(xué)生的學(xué)習(xí)熱情，鞏固對(duì)上面總結(jié)結(jié)論的認(rèn)識(shí)。

七、例題講解 2 例1:已知二次函數(shù)y=ax+bx+c(a?0)的對(duì)稱(chēng)軸是x=2,它與x軸的一個(gè)交 2點(diǎn)坐標(biāo)是(4，0)，則方程ax+bx+c=0的兩個(gè)解是__________ 設(shè)計(jì)思路:鼓勵(lì)學(xué)生自主思考，然后小組討論，派代表上講臺(tái)講解。

八、鞏固練習(xí)

2(1)拋物線(xiàn)y=ax+bx+c(a?0)的圖象全部在x軸下方的條件是()22(A)a,0 b,4ac?0(B)a,0 b , 4ac,0 22(C)a,0 b , 4ac,0(D)a,0 b , 4ac,0(2)下列函數(shù)中其圖象與x軸有兩個(gè)交點(diǎn)的是()11112222(A)y=()x23+155(B)y=()x+23+155(C)y=()x23155(D)y=()x+23+1554444 appearance of the weld appearance quality technical requirements of the project must not have a molten metal stream does not melt the base metal to weld, weld seam and heat-affected zone surface must not have cracks, pores, defects such as crater and ash, surface smoothing, weld and base metal should be evenly smooth transition.Width 2-3 mm from the edge of weld Groove.Surface reinforcement should be less than or equal to 1 + 0.2 times the slope edge width, and should not be greater than 4 mm.Depth of undercut should be less than or equal to 0.5 mm, total length of the welds on both sides undercut not exceed 10% of the weld length, and long continuous should not be greater than 100 mm.Wrong side should be less than or at 0.2T, and should not be greater than 2 mm(wall thickness mm t)incomplete or not allow 7.5 7.5.1 installation quality process standards of the electrical enclosure Cabinet surface is clean, neat, no significant phenomenon of convex, close to nature, close the door.7.5.2 Cabinet Cabinet face paints no paint, returned to rusted, consistent color.7.5.3 uniform indirect gap from top to bottom, slot width <1.5mm 7.5.4 adjacent Cabinet surface roughness is 0.7.5.5 the cabinets firmly fixed, crafts beautiful.7.5.6 Cabinet surface gauge, switch cabinet mark clear, neat, firm paste.7.5.7 Terminal row of neat, is reliable, the appearance is clean and not damaged.7.5.8 cables neat and clean, solid binding, binding process in appearance.7.5.9 the first cable production firm, crafts beautiful, clear signage does not fade.7.5.10 fireproof plugging tight, no cracks and pores.7.6 7.6.1 of the standard electrical wiring quality technology cable a, the multi-core wire bunch arrangement should be parallel to each other, horizontal wire harness or wire should be perpendicular to the longitudinal multi-core wire bunch.The distance between the wire harness and wire harness symmetry, and as close as possible.B-core wiring harness into round, multi-core wire bunch used g wire binding, fastening

七、拓展提高:

21、已知二次函數(shù)y=ax+bx+c(a?0)的圖象 如圖所示，根據(jù)圖象回答下列問(wèn)題: 2(1)方程ax+bx+c=0的兩個(gè)解是__________ 2(2)方程ax+bx+c=4的兩個(gè)解是__________ 設(shè)計(jì)思路:讓學(xué)生對(duì)二次函數(shù)和一元二次方程的關(guān)系的認(rèn)識(shí)上升高度。

22、你會(huì)利用二次函數(shù)的圖象求出一元二次不等式x,x,2，0的解集嗎,(看課堂時(shí)間情況決定是否出示)

八、課堂小結(jié)，提高認(rèn)識(shí)

函數(shù) 方程 22ax+bx+c=0(a ?0)y=ax+bx+c(a?0)橫坐標(biāo)的

值 圖象與x軸交點(diǎn) 根 個(gè)數(shù)

一個(gè)關(guān)系:二次函數(shù)圖象與一元二次方程根的關(guān)系: 兩種思想:函數(shù)與方程互相轉(zhuǎn)化的思想;數(shù)形結(jié)合思想(設(shè)計(jì)思路:用精煉的語(yǔ)言，使得學(xué)生記憶簡(jiǎn)便，而且印象加深，同時(shí)讓學(xué)生在 總結(jié)中反思，完成升華。學(xué)生再次齊讀華羅庚名言，下課。

九、布置作業(yè)，鞏固提升

十、板書(shū)設(shè)計(jì)

課題:??.課題:??.方程與函數(shù)轉(zhuǎn)化 例1: 方程與函數(shù)轉(zhuǎn)化 例1: 函數(shù) 方程 22y=ax+bx+c(a?0)ax+bx+c=0(a ?0)橫坐標(biāo)的

值 圖象與x軸交點(diǎn) 根 個(gè)數(shù) 數(shù)形結(jié)合 數(shù)形結(jié)合

appearance of the weld appearance quality technical requirements of the project must not have a molten metal stream does not melt the base metal to weld, weld seam and heat-affected zone surface must not have cracks, pores, defects such as crater and ash, surface smoothing, weld and base metal should be evenly smooth transition.Width 2-3 mm from the edge of weld Groove.Surface reinforcement should be less than or equal to 1 + 0.2 times the slope edge width, and should not be greater than 4 mm.Depth of undercut should be less than or equal to 0.5 mm, total length of the welds on both sides undercut not exceed 10% of the weld length, and long continuous should not be greater than 100 mm.Wrong side should be less than or at 0.2T, and should not be greater than 2 mm(wall thickness mm t)incomplete or not allow 7.5 7.5.1 installation quality process standards of the electrical enclosure Cabinet surface is clean, neat, no significant phenomenon of convex, close to nature, close the door.7.5.2 Cabinet Cabinet face paints no paint, returned to rusted, consistent color.7.5.3 uniform indirect gap from top to bottom, slot width <1.5mm 7.5.4 adjacent Cabinet surface roughness is 0.7.5.5 the cabinets firmly fixed, crafts beautiful.7.5.6 Cabinet surface gauge, switch cabinet mark clear, neat, firm paste.7.5.7 Terminal row of neat, is reliable, the appearance is clean and not damaged.7.5.8 cables neat and clean, solid binding, binding process in appearance.7.5.9 the first cable production firm, crafts beautiful, clear signage does not fade.7.5.10 fireproof plugging tight, no cracks and pores.7.6 7.6.1 of the standard electrical wiring quality technology cable a, the multi-core wire bunch arrangement should be parallel to each other, horizontal wire harness or wire should be perpendicular to the longitudinal multi-core wire bunch.The distance between the wire harness and wire harness symmetry, and as close as possible.B-core wiring harness into round, multi-core wire bunch used g wire binding, fastening

第三篇：函數(shù)與方程知識(shí)點(diǎn)總結(jié)[范文]

在中國(guó)古代把數(shù)學(xué)叫算術(shù)，又稱(chēng)算學(xué)，最后才改為數(shù)學(xué)。數(shù)學(xué)分為兩部分，一部分是幾何，另一部分是代數(shù)。小編準(zhǔn)備了高一數(shù)學(xué)函數(shù)與方程知識(shí)點(diǎn)，希望你喜歡。

一、函數(shù)的概念與表示

1、映射

(1)映射：設(shè)A、B是兩個(gè)集合，如果按照某種映射法則f，對(duì)于集合A中的任一個(gè)元素，在集合B中都有唯一的元素和它對(duì)應(yīng)，則這樣的對(duì)應(yīng)(包括集合A、B以及A到B的對(duì)應(yīng)法則f)叫做集合A到集合B的映射，記作f：AB。注意點(diǎn)：(1)對(duì)映射定義的理解。(2)判斷一個(gè)對(duì)應(yīng)是映射的方法。一對(duì)多不是映射，多對(duì)一是映射

2、函數(shù)

構(gòu)成函數(shù)概念的三要素 ①定義域②對(duì)應(yīng)法則③值域

二、函數(shù)的解析式與定義域

1、求函數(shù)定義域的主要依據(jù)：(1)分式的分母不為零;

(2)偶次方根的被開(kāi)方數(shù)不小于零，零取零次方?jīng)]有意義;(3)對(duì)數(shù)函數(shù)的真數(shù)必須大于零;

(4)指數(shù)函數(shù)和對(duì)數(shù)函數(shù)的底數(shù)必須大于零且不等于1;

2求函數(shù)定義域的兩個(gè)難點(diǎn)問(wèn)題

(1)已知f(x)的定義域是[-2,5],求f(2x+3)的定義域。

(2)已知f(2x-1)的定義域是[-1,3],求f()x的定義域

三、函數(shù)的值域

1求函數(shù)值域的方法

①直接法：從自變量x的范圍出發(fā)，推出y=f(x)的取值范圍，適合于簡(jiǎn)單的復(fù)合函數(shù);②換元法：利用換元法將函數(shù)轉(zhuǎn)化為二次函數(shù)求值域，適合根式內(nèi)外皆為一次式;

③判別式法：運(yùn)用方程思想，依據(jù)二次方程有根，求出y的取值范圍;適合分母為二次且xR的分式;

④分離常數(shù)：適合分子分母皆為一次式(x有范圍限制時(shí)要畫(huà)圖);⑤單調(diào)性法：利用函數(shù)的單調(diào)性求值域;⑥圖象法：二次函數(shù)必畫(huà)草圖求其

四、函數(shù)的奇偶性

1.定義: 設(shè)y=f(x)，xA，如果對(duì)于任意xA，都有f(?x)?f(x)，則稱(chēng)y=f(x)為偶函數(shù)。

如果對(duì)于任意xA，都有f(?x)??f(x)，則稱(chēng)y=f(x)為奇函數(shù)。

2.性質(zhì)：

①y=f(x)是偶函數(shù)?y=f(x)的圖象關(guān)于y軸對(duì)稱(chēng), y=f(x)是奇函數(shù)?y=f(x)的圖象關(guān)于原點(diǎn)對(duì)稱(chēng),②若函數(shù)f(x)的定義域關(guān)于原點(diǎn)對(duì)稱(chēng)，則f(0)=0

高一數(shù)學(xué)函數(shù)與方程知識(shí)點(diǎn)就為大家介紹到這里，希望對(duì)你有所幫助。

[函數(shù)與方程知識(shí)點(diǎn)總結(jié)]相關(guān)文章：

第四篇：“函數(shù)與方程思想”案例分析

教學(xué)設(shè)計(jì)案例分析

——“函數(shù)與方程思想”案例

一．主題

函數(shù)與方程是中學(xué)數(shù)學(xué)的重要概念，他們之間有著密切的聯(lián)系；函數(shù)與方程的思想是中學(xué)的基本思想，主要依據(jù)題意，構(gòu)造恰當(dāng)?shù)暮瘮?shù)，或建立相應(yīng)的方程來(lái)解決問(wèn)題。函數(shù)思想在解題中的應(yīng)用主要表現(xiàn)在兩個(gè)方面：一是借助有關(guān)初等函數(shù)的性質(zhì)，解有關(guān)求值，解（證）不等式，解方程以及討論參數(shù)的取值范圍等問(wèn)題；二是在問(wèn)題的研究中，通過(guò)建立函數(shù)關(guān)系式或構(gòu)造中間函數(shù)，把所研究的問(wèn)題轉(zhuǎn)化為討論函數(shù)的有關(guān)性質(zhì)，達(dá)到化難為易，化繁為簡(jiǎn)的目的。函數(shù)與方程的思想是歷年高考的重點(diǎn)和熱點(diǎn)。

1.函數(shù)的思想

用運(yùn)動(dòng)和變化的觀(guān)點(diǎn)，集合與對(duì)應(yīng)的思想分析和研究具體問(wèn)題中的數(shù)量關(guān)系，建立函數(shù)關(guān)系或構(gòu)造函數(shù)，運(yùn)用函數(shù)的圖像和性質(zhì)去分析問(wèn)題，轉(zhuǎn)化問(wèn)題使問(wèn)題獲得解決，函數(shù)思想是對(duì)函數(shù)概念的本質(zhì)認(rèn)識(shí)。

2.方程的思想

在解決問(wèn)題時(shí)，用事先設(shè)定的未知數(shù)溝通問(wèn)題中所涉及的各量間的等量關(guān)系，建立方程或方程組，求出未知數(shù)及各量的值，或者用方程的性質(zhì)去分析，轉(zhuǎn)化問(wèn)題，使問(wèn)題獲得解決。

3.函數(shù)的思想與方程的思想的關(guān)系

在中學(xué)數(shù)學(xué)中，很多函數(shù)的問(wèn)題需要用方程的知識(shí)和方法來(lái)支持，很多方程的問(wèn)題需要用函數(shù)的知識(shí)和方法去解決。對(duì)于函數(shù)，當(dāng)

時(shí)，就轉(zhuǎn)化為方程，也可以把函數(shù)

看作二元方程，函數(shù)與方程可相互轉(zhuǎn)化。

4.函數(shù)與方程的思想在解題中的應(yīng)用

（1）函數(shù)與不等式的相互轉(zhuǎn)化，對(duì)函數(shù)，當(dāng)

時(shí)，就化為不等式，借助于函數(shù)的圖像和性質(zhì)可解決有關(guān)問(wèn)題，而研究函數(shù)的性質(zhì)也離不開(kāi)不等式。，當(dāng)

時(shí)，就化為不等式，借助于函數(shù)的圖像和性質(zhì)可解決有關(guān)問(wèn)題，而研究函數(shù)的性質(zhì)也離不開(kāi)不等式。

時(shí)，就化為不等式，借助于函數(shù)的圖像和性質(zhì)可解決有關(guān)問(wèn)題，而研究函數(shù)的性質(zhì)也離不開(kāi)不等式。，借助于函數(shù)的圖像和性質(zhì)可解決有關(guān)問(wèn)題，而研究函數(shù)的性質(zhì)也離不開(kāi)不等式。

（2）數(shù)列的通項(xiàng)與前

項(xiàng)和是自變量為正整數(shù)的函數(shù)，用函數(shù)的觀(guān)點(diǎn)去處理數(shù)列問(wèn)題十分重要。

項(xiàng)和是自變量為正整數(shù)的函數(shù)，用函數(shù)的觀(guān)點(diǎn)去處理數(shù)列問(wèn)題十分重要。

（3）解析幾何中的許多問(wèn)題，需要通過(guò)解二元方程組才能解決。這都涉及二次方程與二次函數(shù)的有關(guān)理論。

（4）立體幾何中有關(guān)線(xiàn)段，角，面積，體積的計(jì)算，經(jīng)常需要運(yùn)用列方程或建立函數(shù)表達(dá)式的方法加以解決，建立空間直角坐標(biāo)系后，立體幾何與函數(shù)的關(guān)系更加密切。

二．背景

此案例的背景主要是：這是一堂與函數(shù)與方程思想有關(guān)的中學(xué)數(shù)學(xué)課，雖然本節(jié)教材是實(shí)施新的課程改革，但是這節(jié)內(nèi)容與老教材的內(nèi)容基本一致。選用此案例的原因是雖然該案例的授課老師授課時(shí)是一節(jié)平常課，采用的上課方式是組討論式，但是該授課老師以前曾有過(guò)用此節(jié)內(nèi)容開(kāi)公開(kāi)課的經(jīng)歷，當(dāng)時(shí)采用的上課方式是普通的啟發(fā)式教學(xué)。通過(guò)此案例我們可以將其進(jìn)行分析比較，進(jìn)而得到結(jié)果。

三．情景描述

四．教學(xué)反思研究

五．教學(xué)設(shè)想

第五篇：研究性學(xué)習(xí)14 函數(shù)與方程

2013屆高三理科數(shù)學(xué)研究性學(xué)習(xí)（14）

專(zhuān)題十一：函數(shù)與方程相關(guān)問(wèn)題研究（復(fù)合函數(shù)的根的問(wèn)題研究）

例：（教學(xué)與測(cè)試第4課時(shí)）已知函數(shù)f(x)?x2?x?q，集合A?xf(x)?0,x?R，??B??xf(f(x))?0,x?R?.（1）若q??2，試求集合A,B

（2）若B為單元素集，試求q的值.變式1：已知c?0，函數(shù)f(x)??cx2?cx，g(x)?x3?cx2?cx，如果函數(shù)y?f(x)與函數(shù)y?g(f(x))有相同的零點(diǎn)，試求實(shí)數(shù)c的取值范圍；

變式2：（2007年江蘇高考）已知a，b，c，d是不全為零的實(shí)數(shù)，函數(shù)f(x)?bx2?cx?d，）g(x)?ax3?bx2?cx?d，方程f（x）=0有實(shí)根，且f（x）=0的實(shí)數(shù)根都是g（f（x）

=0的根，反之，g（f（x））=0的實(shí)數(shù)根都是f（x）=0的根

（1）求d的值；（2）若a=0，求c的取值范圍；

變式3：（2012年江蘇高考）已知a，b是實(shí)數(shù)，1和?1是函數(shù)f(x)?x3?ax2?bx的兩個(gè)極值點(diǎn)．（1）求a和b的值；（2）設(shè)函數(shù)g(x)的導(dǎo)函數(shù)g?(x)?f(x)?2，求g(x)的極值

2]，求函數(shù)y?h(x)的零點(diǎn)個(gè)數(shù)． 點(diǎn)；（3）設(shè)h(x)?f(f(x))?c，其中c?[?2，