( )서술특쫑 3학년해설_교사용.pdf

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2 . 3 ab;ba;(b+0) 0 p. 00 ' 00="ç0 =0 "ç3.h9='4=" = ' 8=" 9 =9 9 ;5@; 'ß -' 0. 3'6 49=" 7 =7' 49-'7 #(-5) =5(-5) ' 5=" 5 =5 a='7b=-'7c=5a+b+c=5 a+b+c=5 4 A D E F p '9'9=" 3 =3 9= 39=3 0 ' 6=" 4 =4' 6'4=" = (-7) =49(-7) -' 49=-" 7 =-7 a=b=-7 a-b=-(-7)=9 a-b=9 3 :3 : 3 =4 : 9 39 cm 9 (4+9) _39=7 cm ' 7="ç3 3 =3'3 cm 3'3 (cm) 4

3 A D E aa-a- a-a- 3 <a<a->0a-<0 " (a-) +" (a-) =a--(a-)= 0 p. 3 ;3!; a-a- A a-a- D 0 y a>bab<0a>0b<0 " (-b) +" (b-a) -"ç4b =" (-b) +" (b-a) -"ç(b) -b>0b-a<0b<0 " (-b) +" (b-a) -"ç(b) =-b-(b-a)-(-b)=a-b a-b xyx+x-y-y x+x-y-y p a>bab<0a>0b<0 -a<0-b>0 " a -" b +" (-a) +" (-b) =a-(-b)-(-a)+(-b) =a a a>bab<0a>0b<0 " (-a) +" (b-3a) -" 4b =" (-a) +" (b-3a) -" (b) -a<0b-3a<0b<0 " (-a) +" (b-3a) -" (b) =-(-a)-(b-3a)-(-b) =4a+b 4a+b 3 -<x<<yx+>0x-y<0-y<0 " (x+) +" (x-y) -" (-y) =x+-(x-y)+(-y) = 4 x+x-y-y A x+x-y-y 3 D 3

4 c a+b+c p 'ƒ43a' 63bc!'ƒ43a=" 3 5 _a a=3_ 63b=" 3 _7_b b=7_ b=7b 'ƒ43a-' 63b="ç3 6 -" 3 _7 =7-=6c=6 a+b+c=3+7+6=6! 'ƒ50x=" _3_5 _x x=_3_ : ] :=æ 3 _7 y y=73 _7=63 y=763 a=6b=7a+b=3 a+b=3 p 'ƒ6-x 6-x=965 x=0756 M=6m=M+m=7 M+m= ab ab c a+b+c A 4363 ab D ab E c F a+b+c G 400n 0 ' 8ab=" 3 _ab ab=_ #ab=8(ab)=(36)(63) (ab)=()()(4)4)(36)(63) abc 4363 ab ab ' n' 3n' nnn ' 3n' nn ' n' 3n' nn 3!' nn=_ n_ =_ =8y_4 =39 3nn=3_ n3_ =33_ =y3_ =363 4

5 #' n=" _3_nn=3_ n3_ =33_ =y3_ n' 3n' n n400-4-= p. <A< 4 ' n' 3n' nnn ' 3n' nn ' n' 3n' nn 0.56 x+ 5. x+< x<8.68 < x<8.68x A ' n' 3n' nnn 6 ' 3n' nn D n E 3 x '7 7 <x< '3 3 3'7 7'3 <x< 3'7=' 637<3'7<8 7'3=' 47<7'3<3 p. 0 x=; ;;!);;!!; ; ;;!);;!!; 4>' 4 Æ;4#;<Æ;8&; 3'5+'<3+'5 44>+' <' x 6 6<x 368<x 8 8<x 8x90y8 M=8m=9M-m=9 M-m=9 4 A D E F 5

6 (xy) xy xy (xy) 3x+y AD=(3_3)-4_{;!; }=5 AD5'5 '5 A =AF ='5AD =AE ='5 E'5E(0-'5) F'5F(0+'5) E-'5F'5 3 4<xy<9 4<xy<9 4<xy<9<xy<;(; p. 08 (xy)=(3)(3)(4)()(4) 3x+y =' 498=' 6478 ' 50' 5' 5y' 6' xy xy (xy) 3x+y A (xy) xy xy D (xy) E x+y F 0 AD=(3_3)-4_{;!; }=5 AD5 '5 '5 EFGH=(4_4)-4_{;!;_3_}=0 EFGH0 ' 0 ' 0 3AD =AP ='5 EF =EQ =' 0 P-4'5P(-4-'5) Q' 0Q(+' 0) P-4-'5 Q+' 0 ADPQ 05 AD ab 3a-3b p. 06 '5 3' P+'5 Q-'5 3 AD=(3_3)-4_{;!; }=5 AD5 '5 '5 6

7 A =AQ ='5AD =AP ='5 P'5P(-'5) Q'5Q(+'5) a=-'5b=+'5 3a-3b =(-'5)-3(+'5)=4-'5-6-3'5 =--5'5 --5'5 A S S S S a D S b E OE EF F F G 4 AD ab 3a-3b A AD ab D a-3b E 06 p. 0 OE EF S S S S a S b 3OE EF 3F 3<' 5<4 4<'6<5 3<+'<3 3' '5-6 33'3-43-'6 4<4-'5< 3 S =;!;_8_8=3S =;!;S =6S =;!;S =8 S =3S =6S =8 ;!;a =6a =3a=4'(a>0) ;!;b =8b =6b=4(b>0) a=4'b=4 3OE =OA +A +E =8+4'+4=+4' EF =E =b=4 F(+4'4) F(+4'4)!'5=' <'5<5 5-'5b= a+b ='5-4+ ='5 a+b ='5 p. 4 S S S S a S b 3OE EF 3F 0!<'3<-<-'3<-3<5-'3<4 3<'3<4 '3'3-3b='3-3 a+b=3+'3-3='3 a+b='3 7

8 0 7' 5084' 85 ' 50' 50-7=5'-7 ' 8' 8-4=3'-4 f(50)=5'-7 f(8)=3'-4 f(50)-f(8)=5'-7-(3'-4)='-3 '-3 3 x-3y 5x-4y =x-3y=0x-8y5y=8xy=;5*;x æ 3x+y 3x-y y=;5*;x æ 3x+y 3x+;5*;x 3x-y = = 3x-;5*;x : 5 :x =æ : 7 : ;5&;x 3+' 0 a 9-'a b 3a-b <æ : 7 :<æ : 7 : 4 3 3<' 0<46<3+' 0<7 3+' 06 a=6 A <'6<3-3<-'6<-6<9-'6<7 9-'69-'6-6=3-'6 b=3'6 D 3a-b=6-(3-'6)='6 E a-b='6 F 4 3+' 0 a 9-'a b 3a-b A 3+' 0 a D 9-'a E b F a-b G p. 4 0!55 #" (-36) =366 a=5b=-;4#;c=6 a+4b+c=5+4_{-4#;}+6=8 a+4b+c=8 A " -36 abc 3 D a+4b+c E x m ('5) +('6) =5+6= m x =x=' m(x>0) ' m 8

9 A D 06 9<3a<493<a<; 3ª; 3<a<; 3ª;a456y63 M=6m=4M_m=6_4=64 M_m=64.0H= 0-0 =;9(0@;=;4$5^;0.H3=;9#;=;3!; 90 æ ;4$5^;_;[};=;3!; ;4$5^;_;[};=;9!;;[};=;9!;_;4$6%;=;4 6; x=46y=5x-y=4 x-y=4 A a D Mm E M_m F A.0H0.H3 ;[}; D xy E x-y F a<b<0a<0 -b>0 a-b<0 b-a>0 "ça -" (-b) +" (a-b) -" (b-a) =(-a)-(-b)-(a-b)-(b-a) =-a+b-a+b-b+a =-a+b -a+b 07 AD=(4_4)-4_{;!;_3_}=0 AD0 ' 0 P' 0P(-' 0 Q' 0Q(+' 0 a=-' 0b=+' 0 a-b=-' 0-+' 0=-' 0 a-b=-' 0 A AD ab D a-b E A a-ba-bb-a D E 05 'ƒ4-x4-x=46 x=4 4 A 4-xx x D 08!<'5<34<+'5<5 +'5+'5-4='5- <'5<5-5<-'5<-4 <6-'5< 6-'56-'5-=5-'5 b=5-'5 a+b='5-+5-'5=3-'5 a+b=3-'5 A +'5 6-'5 D ab E a+b F 9

10 07. 8 ;5@; ab ;5 0;a p. 8 ' 3='ƒ3._00=0'ƒ3.=0a 3. 'ƒ0.3=æ 00 = 'ƒ3. 0 =; 0;b ' 3+'ƒ0.3=0a+; 0;b 4 3'3 x ' 48-' 300 x A 3!3'3=' 75<3'3<6 48-' 300=4'3-0'3=-6'3 3'3=x+5-6'3=(-)_3'3=-(x+5)=-x-0 -x-0 3'3 x D ' 48-' 300 E x F 0a+; 0;b ab p. 0 ' 500a 'ƒ b ' 0.a ab 0 0 'ƒ0.005=æ ;0 0º00;= " _5 " 00 = 5' 00 =; 0;' k=; 0; 'ƒ0.84=æ ;0#0*0$0;= " 7 _3 " 00 = (')7 _'3 =;0!0;a 7 b 00 ;0!0;a 7 b{;5 0;a 5 b; 5;a 3 b; 5;ab} x 3'3 x ' 48-' 300 x 3 ' 500=" 5_0 =0'5=0a 'ƒ =æ ;00 0º000;= ' 50 " 000 = ' =;0 00;b 'ƒ0.=æ ; 0º0;= " _5 "ç0 = '5 0 = '5 5 =;5!;a ' 500+'ƒ ' 0.=0a+;0 00;b-;5!;a : 5ª:a+;0 00;b =: 5ª:a+;0 00;b 4 ' 500a 'ƒ b ' 0.a ab 0

11 A ' 500a 'ƒ b D 'ß0.a E ab F 0 f(x)= 'ƒx++'ßx = _('ƒx+-'ßx) ('ƒx++'ßx)('ƒx+-'ßx) ='ƒx+-'x f()='-' f()='3-' f(3)='4-'3 + f(80)=' 8-' 80 f()+f()+f(3)+y+f(80) =' 8-'=9- = p. 5'3- -'3 ab a-b ;#;' ' ' ' 30 9 '5+' 6-3'3 3 '- = _('+) ('-)('+) ='+ <'<<'+<3 '+a= '+-='-b='- 'a-b='-('-)= 'a-b= 3!5'3=' 758<5'3<96<5'3-<7 -'3 = _(+'3) (-'3)(+'3) =+'3 <'3<3<+'3<4 +'3+'3-3='3- b='3- a-b=_6-('3-)=3-'3 a-b=3-'3 4 5'3- -'3 ab a-b p '7 = (3-'7) (3+'7)(3-'7) =3-'7 3-'7=a+b'7 a=3b=-ab a +b =3 +(-) =0 a +b =0 A 5'3- D -'3 E ab F a-b G

12 æ {;; 4 ;;-'} -" ('-3) =;; 4 ;;-'+('-3)=;4!;+' A+'=;4!;+'A=;4!;= A=;4!;= 3 : :' x cm 'x 3x+3'x=3+6'(3+3')x=3+6' x= +' +' = (+')(-') (+')(-') = -3+' =3-' - (3-') cm p. 8 0!'å4+ '3 '3_' '6 ='6+ ='6+ ' '_' ' 4-3'3 '6 = ' 4-3 ' = ' 4-3_' '_' = ' 4-3' =-;4%;' a=;%;b=-;4%;a-8b=_;%;-8_{-;4%;}=5 4 A D 3 E 0 a-8b=5!a= 3'-'3 = (3'-'3)'3 '3 '3_'3 = 3'6-3 '3-' '3+' = ('3-') ('3+')('3-') =5-'6 A-='6--(5-'6)=-+5'6 A-=-+5'6 A 09 -'3 6'3 33'3 48'5 3'5-3 -'3 3-' p '6 ;; 4 ;;>';; 4 ;;-'>0'<3'-3<0 3 Aabc!a =5a=' =45b='4å5b=3'5(b>0) #c =5c='5(c>0) A5'5 m 3'5 m '5 m {a+(a+b+c)} =4a+b+c =4_5'5+_3'5+_'5=8'5 8'5 m 4 A

13 A A 3 D D D '+4'3 0!A=4'-'(4-' ' '3 - ' 0 '3 ='6_ ' - '5 =3-'5 A+='5+(3-'5)=6 A+=6 p Dbcd ='ß50-4 ' +'8=5'-'+'=5'!b=3-'-=-' A+=0+' #d=(-')-('-)=3-' D-''- 3-' Db+c+d b+c+d=-'+'-+3-'=4-' 4-' 4 a+b=-5 D D 0 0 A='6 { '6-5 '3 }+3" 3 +'=-5'+9+'=0-4' '(a-'3)+'åå0('5-b'å5) =a'-'6+0'-5b'6 =(a+0)'-(+5b)'6 a+0=4+5b=6a=-6b= A 0 D D D 3'+6 '5-'6 3'3 p '6- ' {'+ '8 - ' } 3 '6- ' ('3+')+ 4 ' { '+ '8 - ' } =('3-')('3+')+' {'+ ' - ' } =3-+'_ =+4' +4' 4 '6- ' {'+ '8 - ' } 3

14 A '6- ' {'+ '8 - ' } D E a=-4 (4+a'5)(3-'5) =-4'5+3a'5-5a =(-5a)+(3a-4)'5 (-5a)+(3a-4)'5 3a-4=0 a=;3$; V S 3 V=('3+'5)_'3_'5=3'5+5'3 V=(3'5+5'3) cm 3 =('3+'5)_'3=3+'åå5 =(4'3+'5)_'5=4'åå5+0 S =_+=(3+'å5)+4'å5+0 =6+6'å5 S=(6+6'å5) cm p '(k+3')-'3('3-'6) =k'+6-3+3' =3+(k+3)' 3+(k+3)'k+3=0 k=-3 'å {'6- '3 }- a ' (-'8)=6'--a'+a =(a-)+(6-a)' (a-)+(6-a)' 6-a=0 a=6a-=_6-=0 a=60 4 V S A V D S E x x 3 '4å5+ 0 '5- -'5å0_'+x'5 =3'5+ 0('5+) -0+x'5 4 =3'5+;%;'5+;%;-0+x'5 =-;; ;;+{;; ;;+x}'5 p. 054 a=-8b= -;; ;;+{;; ;;+x}'5 ;; ;;+x=0 x=-;; ;; 4

15 4 x A D x E A 4 D ab E a+b F ab ab a+b ' 36 p ! (a'5+3)+(b+'5)=(b+3)+(a+)'5 (b+3)+(a+)'5 a+=0 (a'5+3)(b+'5)=ab'5+5a+3b+3'5 =(5a+3b)+(ab+3)'5 (5a+3b)+(ab+3)'5 ab+3=0 ab=-3!@ a=-b=3 a+b= 4 x= -'3 = +'3 (-'3)(+'3) =+'3 y= +'3 = -'3 (+'3)(-'3) =-'3 x+y=4xy= x -xy+y =(x+y) -3xy=4-3_=3 x -xy+y =3 p ab a+b 0 a= '5+'3 = ('5-'3) ('5+'3)('5-'3) ='5-'3 b= '5-'3 = ('5+'3) ('5-'3)('5+'3) ='5+'3 a+b='5ab= a+b ab = '5 ='5 a+b ab ='5 5

16 0 x= +'5 = -'5 (+'5)(-'5) =-+'5 y= -'5 = +'5 (-'5)(+'5) =--'5 x+y=-4xy=- x +y =(x+y) -xy=(-4) -_(-)=8 x +y =8 ab a+bab 3 a= -'3 +'3 = (-'3) (+'3)(-'3) =7-4'3 b= +'3 -'3 = (+'3) (-'3)(+'3) =7+4'3 a+b=4ab= a +ab+b =(a+b) -ab=4 -=95 a +ab+b =95 4 ab a+bab <'<4<3+'<5 3+'4a=4 3+'-4='-b='- a+b+=4+('-)+=4+' a-b-=4-('-)-=4-' a+b+ + a-b- = 4+' + 4-' = (4-')+(4+') (4+')(4-') ;7$; =; 4;=;7$; ' ab ab A 7 3-' D ab E ab F A ab a+bab D E 7 3-' ab ab ' = 7(3+') (3-')(3+') =3+' p. 06 0!'ƒ00=" _0 =0' 00 = '.3 0 =;5!;'.3=;5!;a 'ƒ00+'ƒ0.05=0b+;5!;a ;5!;a+0b A 'ƒ00b 'ƒ0.05a D ab E 6

17 0 aæ : aı:-bæ ;8Åb;=' ab-æ :Å8ı: 9 =' 44-'9(ab=7) =-3 =9 A ab D -'3 = +'3 (-'3)(+'3) =+'3 <'3<3<+'3<4 +'33a=3 +'3-3='3-b='3- a-b=3-('3-)=4-'3 a-b=4-'3 A -'3 D ab E a-b F 3'- 3-' =(3'-)(3+') (3-')(3+') =9+7' 9+7'=x+y'x=9y=7xy x-y= A 05 3'- 3-' xy D x-y E ' -'3+4'7+' 63 ='3-'3+4'7+3'7 ='3+7'7 '3+7'7=A'3+'7 A= =7(A) A+= ' ' 7-' 7 ('+'3)- =3'('+'3)-(3-'6) '3 =6+3'6-3+'6 =3+5'6 3+5'6=a+b'6a=3b=5ab ab=5 A 07 ab D ab E (-'3)(a'3-5) =a'3-0-6a+0'3 =-0-6a+(a+0)'3-0-6a+(a+0)'3 a+0=0 a=-5 A 08 D a E x= 7+4'3 = 7-4'3 (7+4'3)(7-4'3) =7-4'3 x-7=-4'3 (x-7) =(-4'3) x -4x+49=48 x -4x+48=47 47 A x D E p. 064 A A D A+ E ' 4_'=4' (3+5)=6 4_'=4' =4'+6+4'=6+8' 6+8' 7

18 A D ' 4+'+'=4+4' 4'++'+=4+6' =(4+4')+(4+6')=8+0' 8+0' x -4x+a=(x+)(x+m) x-4=m+m=-5 a=m=-5 a=-5 3x +bx-x 3-3x +bx-=(x+)(3x-) xb= b= A D p x +5x+6 x +5x+6=(x+3)(x+) x+3x+ x+3x+ 3 {(x+)+(x+3)}=4x+0 4x+0. 0!a +a+b-b =a -b +a+b =(a+b)(a-b)+(a+b) -b =a(b-)+b(b-) =(a+b)(b-)!@a+b a+b 3 a p. 070 x -3xx -x-5 x -x+a a xy(x+3y-) (a-3)(b+) 3(x-) 4(3x+) 5(4x+y)(4x-y) 7(x-3)(3x-) 6(x+3)(x-6) 8(a+)(b+) 3 x -3x=x(x-3)x -x-5=(x+5)(x-3) x-3 x -x+a=(x-3)(x+m) x-=m-3m= a=-3m=-3_=-3 a=-3 8

19 4 x -3xx -x-5 x -x+a a A x -3xx -x-5 D x -x+a E a F p. 074 (x-)(x+5)+k=x +3x+k-0 k-0={;#;} =;4(;k=; 4ª; k=; 4ª; x x+mx+n amn mn=-5(mn) a 3 x +ax-5x+mx+n mn x +ax-5=(x+m)(x+n) m+n=amn=-5 (mn)(-5)(-53)(-35) (-5)(-5)(3-5)(5-3)(5-) a-4-44 a= x+mx+n amn mn=-5(mn) a p (x-)(8x-)+kx =6x -0x++kx 6x +(k-0)x+ =6x +(k-0)x+ 6x +(k-0)x+ k-0= _4= 8k=8 k=8!4x -6x+a=4{x -4x+;4A;} ;4A;={ -4 } +6x+b={x +8x+;;} ;;={;*;} =6b=3 a=6b=3 a a+3a- A x x+mx+n amn D mn=-5(mn) E a F 3 " a +6a+9+" a -4a+4=" (a+3) +" (a-) -3<a<a+3>0a-<0 " (a+3) +" (a-) =a+3-(a-)=5 5 9

20 4 a+3a- A a+3a- D E 5 x +6x+8 (x-)(x-5) p. 078 a a-;a!;a+;a!;! (x-3)(x+6)=x (x+)(x-5)=x -3x-0-3!@x -3x-8 x -3x-8=(x-6)(x+3) (x-6)(x+3) 3 æ {a+;a!;} -4+æ {a-;a!;} +4 p. 080 =æ a + a -+æ a + a + =æ {a-;a!;} +æ {a+;a!;} 0<a<a-;a!;<0a+;a!;>0 æ {a-;a!;} +æ {a+;a!;} ;a@; 4 =-{a-;a!;}+{a+;a!;}=;a@; a-;a!;a+;a!; A D a-;a!;a+;a!; E F 0 0!x (x+8)(x-3)=x (x+)(x-4)=x -x-8 x-!@x -x-4 A=x -x-4 x -x-4=(x-6)(x+4) (x-6)(x+4)!x (x-)(x-)=x (x-5)(x+)=x -9x-5=-5 #x A= A==-3=-5 x -3x-5=(x-5)(x+) (x-5)(x+) 0

21 !x 4 (x+)(x+)x (x+5)(x-) (x-)(x+)(x +7) =(x -4)(x +7) =x 4 +3x -8 4 (x-)(x+)(x +) =(x -4)(x +) 3 =x 4-3x -4!x x -4 #x 4 x 4 (x+)(x+)=x +3x+ x3!@#x 4 +3x x 4 +3x -4=(x -)(x +4)=(x+)(x-)(x +4) (x+)(x-)(x +4) (x+5)(x-)=x +9x-5-5 #x x!@# x +3x-5 x +3x-5 x +3x-5=(x+5)(x-) (x+5)(x-) 3 4 (x-)(x+)(x +7) (x-)(x+)(x +) 4 (x+)(x+)x (x+5)(x-) A (x+)(x+)x (x+5)(x-) D E F A (x-)(x+)(x +7) (x-)(x+)(x +) D E F 6 (x-)(x+)(x +7) (x-)(x+)(x +) p. 08 (a+)(b-) (x-y+)(x-y-) 3(x+)(x+8) 4(x +3x+) x-6y

22 (x+y)(x+y-5)-6 =A(A-5)-6 x+y=a =A -5A-6 =(A+)(A-6) =(x+y+)(x+y-6) (x+y+)+(x+y-6)=x+y-5 x+y-5 =(A-4)(A+6) =(x +3x-4)(x +3x+6) =(x+4)(x-)(x +3x+6) (x+4)(x-)(x +3x+6) 4 p x -4xy+4y -x+y- =(x-y) -(x-y)- =A -A- x-y=a =(A+)(A-) =(x-y+)(x-y-) a+b+c+d=-+--=-5-5 6(x-y) -7(x-y)-3 =6A -7A-3 x-y=a =(3A+)(A-3) =(6x-3y+)(4x-y-3) (6x-3y+)(4x-y-3) 5(x-5) +3(x-5)(x+3)-6(x+3) =5A +3A-6 x-5=ax+3= =(5A-)(A+3) =(5x-5-x-6)(x-5+3x+9) =(3x-3)(4x+4) =4(3x-3)(x+) 4(3x-3)(x+) 3 x(x+)(x+)(x+3)-4 =x(x+3)(x+)(x+)-4 =(x +3x)(x +3x+)-4 =A(A+)-4 x +3x=A =A +A-4 A abcb<c<a a 65abc 3 abc-ab-ac-bc+4a+4b+4c-8 =a(bc-b-c+4)-(bc-b-c+4) =(a-)(bc-b-c+4) =(a-){b(c-)-(c-)} =(a-)(b-)(c-) 65=3_5_ a-=c-=5b-=3 b<c<a a=3b=5c=7 4 a 65abc A D E a D E 65a, b, c 3 F

23 p. 086 A=".5 -_.5_ =" (.5-0.5) ="ç = A= a -ab+b =(a-b) =( 0 -)( 0 +) =( 0 -)( 0 +)( 0 +) =( 5 -)( 5 +)( 0 +)( 0 +) 5 -=3 5 += A D E p a -b =(a+b)(a-b) A = =(-3)(+3)+(5-7)(5+7)+y +(7-9)(7+9) =-(+3+5+y+7+9) =-_(0_5) =-00 A=-00 05=x _05+ = (x-)x+(x-) 05 - x - = (x-)(x+) (x+)(x-) = x N 3 50=x 50_5_54_55+4 =x(x+)(x+4)(x+5)+4 =x(x+5)(x+)(x+4)+4 =(x +5x)(x +5x+4)+4 =A(A+4)+4 x +5x=A =A +4A+4 =(A+) =(x +5x+) N=x +5x+x=50 N=50 +5_50+=75 N=75 4 x N 3

24 A x D E N F x+y='5x-y=' (x+y+)(x-y+) =('5+)('+) =4' 0+'5+'+ 4' 0+'5+'+ 8 xy 4+'3 35 '5 p. 090 x -y -y-=x -(y +y+) =x -(y+) =(x+y+)(x-y-) x+y=6x-y=4'3 (x+y+)(x-y-)=(6+)_(4'3-)=8'3-7 8'3-7 3!x= +'3 -'3 = (+'3) (-'3)(+'3) =7+4'3 y= -'3 +'3 = (-'3) (+'3)(-'3) y-y -xy +x =x y-xy +x -y =xy(x-y)+(x+y)(x-y) =(x-y)(xy+x+y) x-y=8'3xy=x+y=4 (x-y)(xy+x+y)=8'3_(+4)=0'3 0'3 4 xy p x +xy-6y =(x-y)(x+3y) = '3- _ '3+ = ('3-)('3+) =!x= 3 '5-' = 3('5+') ('5-')('5+') ='5+' y= 3 '5+' = 3('5-') ('5+')('5-') +x+-y =(x+) -y =(x+y+)(x-y+) A xy D E F (ab) A= (ab) 4

25 3 " a -55=b a -55=b a -b =55(a+b)(a-b)=55 (ab)=(83)(87) 4 A= (ab) A A= D (ab) E 0 6a +7a-3=(3a-)(a+3) (a+3) m (a+3) m a cmb cm pa -pb =p(a+b)(a-b)!p cm +D =A -D =a-b=a-b= p(a+b)(a-b)=6p cm 6p cm A A 9 4x+y p cm p. 094 (9x +4x+6)+(7x +6x+9)=6x +40x+5 6x +40x+5=(4x+5) 4x+5 4x+5 p !A p( )_0=(6.4+.4)_(6.4-.4)p_0 =7.8_5p_0=390p(cm 3 p( )_ =( )_( )p_ =6._5p_=37p(cm 3 )!@A A A 4 A A A D E 0 (6a +a-)+(6a-)=(6a +7a-3) m 5

26 a+b a-b 3 a -ab+b -9=(a-b) -3 =(a-b+3)(a-b-3)!a4(a+b) b a -b =(a+b)(a-b)= a-b= a+b = 4+'5 = (4-'5) (4+'5)(4-'5) =4-'5 (a-b+3)(a-b-3) =(4-'5+3)(4-'5-3) -8'5 4 =(7-'5)(-'5) =-8'5 a+b a-b 0 x +7x-5=(x-3)(x+5) 4x -x+9=(x-3) x-3a=b=-3 ab=-6 A ab D ab E x +7x+k=(x+a)(x+b)a+b=7ab=k (ab)(6)(5)(34)(43)(5) (6) k(ab)=(6)(6) k=ab=6 6 A kab a+b=7(ab) D k E A a+b D a-b E F p x -(8k-)x+49 8k-= _5_7= : k=9-: : A x k D A+=8+5=33 A+=33 05 " x -0x+5+" -x+x =" (x-5) +" (x-) <x<5x-5<0x->0 " (x-5) +" (x-) =-(x-5)+x-=4 4 A a aa D A+ E A x-5x- D E 6

27 06! (x+7)(x-5)=x (x-8)(x+3)=x -5x-4-4!@x +x-4 x +x-4=(x+6)(x-4) (x+6)(x-4) A (x+7)(x-5) (x-8)(x+3) D E A 05=xx 0 {- }{- }{- } y{- } ={-;!;}{+;!;}{-;3!;}{+;3!;}{-;4!;}{+;4!;} =;!;_{;#;_;3@;_;3$;_;4#;_;4%;_y_;ª0;}_;!0!; =;!;_;!0!;=;!0!; ;!0!; D a E y {-; 0;}{+; 0;} 07 (x-y) +5(x-y)-3 =A +5A-3 x-y=a 08 =(A-)(A+3) =(4x-y-)(x-y+3) (4x-y-)(x-y+3) A 09 D (x+y)(x-y)+ =(x+y)(x-y)+(x+y)+(x-y)+ =A+A++x+y=Ax-y= =A(+)++ =(A+)(+) =(x+y+)(x-y+) (x+y+)(x-y+) A (x+y)(x-y)+ D E 05=x 'ƒ_05+ ='ƒ(x-)x+=" x -x+=" (x-) =x-(x->0) a=x-=05-= a= A D E (a-b)a +(b-a)b =(a-b)a -(a-b)b =(a-b)(a -b ) =(a-b)(a-b)(a+b) =(a-b) (a+b) (a-b) =(a+b) -4ab=('5) -4_= (a-b) (a+b)=_'5='5 '5 A D E!x= +'3 = -'3 (+'3)(-'3) =-'3 y= -'3 = +'3 (-'3)(+'3) -y +4x-4y =(x+y)(x-y)+4(x-y) =(x-y)(x+y+4) x-y=-'3x+y=4 (x-y)(x+y+4)=-'3_(4+4)=-6'3-6'3 7

28 3 A xy D E F x y-xy +x-y=4 xy(x-y)+(x-y)=4(xy+)(x-y)=4 x-y=4(xy=4) x +y =(x-y) +xy=4 +_4=4 x +y =4 A x y-xy +x-y=4 x-y D x +y E 4!80 cm cm x -y =300(x+y)(x-y)=300x-y=5 4(x-y)=60 cm 60 cm 5 A x+y x-y D E x +x-6=(x-)(x+3)3x -5x-=(3x+)(x-) x-a =x- =(x+3)+(3x+)=4x+4 AD4x+4 4x+4 6 x m r m!8p m m (r+x) p-r p=44px(r+x)=44x=8 x=8r+8=8r=5 5 m A D E F ab-3a-b+6 =a(b-3)-(b-3) =(a-)(b-3) ab(a-)(b-3)=5 a-b-3 a b (ab)=(38)(74)(-)(-3) A a b(ab) p. 0 5 D (ab) E ab-a-b+4 =a(b-)-(b-) =(a-)(b-) ab(a-)(b-)=6 a-b- a- 3 6 b- 6 3 (ab)=(38)(45)(54)(83) A D AD E A ab(ab) 6 D (ab) E 8

29 0. 3!x +3x-5=0x=a a +3a-5=0a -x-4=0x=b 3b -b-4=0 b+0b3b-;b$;= p. 08 x=0x=- 3x=-;!;x=;3@; x=4x=-!x +4x+4=0x=p p +4p+4=0p -4x+=0x=q 3q -4q+=q -4q=- x=3x=-5 4x=x=;4%; x=x=-;5!; (p +4p-)(3q -4q-)=(-4-)_(--)=5 5 a +6a-3b+;b$;=(a +3a)-{3b-;b$;} 8 4 =_5-=8 x=aa +3a x=b3b-;b$; A x=aa +3a x=b3b-;b$; D E A=0 p x -x-5=x -5x-3x +3x-=0 b=3c=-b+c= b+c= -5ax -0x=x +4(+5a)x +0x+4=0 +5a+0 a+-;5!; x=aa +3a x=b3b-;b$; xy 3 x -5xy-6y =0(x+y)(x-6y)=0 x+y=0 x-6y=0 xy>0x-6y=0x=6y y x +;]{;x=6y y x +;]{;=y 6y +: ] :=+6=8 8 4 xy 9

30 A A=0 xy D E x= a a 3 x= -a+a +3-7=0a -a-=0(a+)(a-)=0 a=-(a+ ) a=- 3x +4x-7=0(x-)(3x+7)=0 p. x=x=-;3&;x=-;3&; x=-;3&; a=4 a=-9x=-5 4 x= a a x= 4-4a-+3a=0-a+=0a= a= a= x -5x+6=0(x-)(x-3)=0 x=x=3x=3 x=3 A x= a D a E F p. 4 0 x=- 6+a+a -6a=0a -5a+6=0(a-)(a-3)=0 a=a=3 a+3=5 5 k x= k k 0 x -3x+=0(x-)(x-)=0x=x= x -3x+=0x= x -x+a=0x=4-+a=0a=- x -x-=0(x+)(x-)=0x=-x= x=- a=-x=- a 3 x= 4k+4-k -4-4k+=0-k +=0k = k=(k+- ) k= x -3x-=0(x-)(x+)=0 x=x=-;!;x=-;!; x=-;!; 30

31 4 x= k k A x= k D k E F 0 {-4_;!;} =4 x -4x+4=+4 (x-) =5 (x-) =5 A=-=5A+=3 A+=3 x +;#;x-;!;=0 x +;#;x=;!; {;#;_;!;} =;ª6; x +;#;x+ ;ª6; =;!;+ ;ª6; {x+;4#;} = ;!6&; x+;4#;= ' 7 4 x= -3 ' 7 4 A=;ª6;=;!6&;= -3 ' 7 4 p. 6 x=3 '5 x= '5 (x-) = (x-) =;#; = 3 4x +8x-=0 3x -x-3=0 3 x -;3@;x-=0 4 x +x-;4!;=0 x +x=;4!; {_;!;} = x +x+=;4!;+ x -;3@;x= {-;3@;_;!;} =;9!; x -;3@;x+;9!;=+;9!; x= ' 0 3 {x-;3!;} =: 9º: x-;3!;= ' 0 3 p. 8 0 x -4x-=0 x -4x= (x+) =;4%; x+= '5 x=- '5 4 - '5 { } = A = 3 D 3

32 A = A -k-={ -k } -k-=k k +k+=0(k+) =0k=- k=- k=- x +x+=0(x+) =0x=- x=- 3 3x +6x-A=0 3 x +x- A 3 =0 x +x= A 3 {_;!;} = x +x+= A 3 + p. (x+) = A+3 3 A== (x+) =;3$; x+= '3 3 x= -3 '3 3 =-3 A===-3 4 = A 0 0 x x +4x+6-;!;m=0 6-;!;m={;$;} 6-;!;m=4m=4 m=4 -a+={ -a+ } -a+=(-a+) -a+=a -a+a =0a=0 a=0 a=0 x +x+=0(x+) =0x=- x=- A = 3 D A E a a a 3 p. 0 3 a -={ -a+ } a -=(-a+) a -=a -a+a +a-3=0(a+3)(a-)=0 a=-3a=a- - a=- a= 8 k= 8 4 a a 3

33 A a D a E A -x +4x=4 D a E ab ab (ab) 0!x -6x+q=0x=37-8+q=0 q=-9 7x +px+q=0p=-q=-9 7x -x-9=0(x+)(7x-9)=0 x=-x=;7(; 3 x -ax+b=0 b={-;a;} b= a 4 a =4b a =4b(ab)()(44) ;3 6;=; 8; ; 8; A p q D 7x +px+q=0pq E F 4 ab (ab) A ab D (ab) E F!x +(k+)x+k=0x=3 +kx+k+=0k=-3x -3x-=0 x -3x-=0 x -3x-=0 A x +(k+)x+k=0x=3 k D E p. 4 0!-x +4x=4x -4x+4=0(x-) =0x= +ax-8=0x=4+a-8=0a= a= x -5x+=0x=aa -5a+=0 a+0aa+;a!;=5 a + ={a+;a!;} -=5 -=3 a a -3a+-;a#;+ a =a + a -3{a+;a!;}+ 9 =3-3_5+=9 33

34 05 A x -5x+=0x=a aa+;a!; D a + a E F G!x= x +4x-=0(x+6)(x-)=0 x=-6x=x=-6 x=-6 08 A k-={ k+ } k-=;4!;(k +k+) 8k-4=k +k+k -6k+5=0(k-)(k-5)=0 k=k=5 A D k E k D A x= a D a E F 06 3x -x+7=0 3 x -4x+;3&;=0 x -4x=-;3&; {-4_;!;} =4 x -4x+4=-;3&;+4 (x-) =;3%; 4. p. 8 x-= ' 5 3 x= ' ' 5 { } 3 x= - ' 3 x= -3 ' 7 07 A = 3 D (x+6)(x-)=kx +4x-k-=0 -k-={;$;} -k-=4k=-6 k=-6 x= - '7 3 x= - '6 x -9x+m=0 x= -(-9) " (-9) -4 m = 9 'ƒ8-8m _ 4 9 'ƒ8-8m = n ' m=33n=9 4 4 m=6n=9 m+n=5 34

35 p x -7x+3=0 x= -(-7) " (-7) -4_3_3 _3 7 ' 3 6 A+=0 = 7 ' 3 6 = A ' A=7=3 6 a x;!; 0 x= -b " b -4ac a a=3b=-c=-b= x= -(-) " (-) -4_3_(-) = ' 5 _3 6 = 5 6 x=-;3@;x= ab n n 3 ax +bx+c=0(b -4acæ0) x a x +;a;x+;a;=0 x +;a;x=-;a; x;!; x +;a;x+{;ıa;} =-;a;+{;ıa;} {x+;ıa;} = b -4ac 4a x+;ıa;= " b -4ac a x= -b " b -4ac a 4 a x;!; 3 x +6x+3=0 x= -6 " _ = -6 '6 =-3 '6 a=-3-'6b=-3+'6(a<b) -'6<n<'6 n ab n n A ab D n E n F A a 5 x=-;3!;x=-5 x;!; D E F p. 3 x= -4 '

36 x=-7x=4 6 6(x-) -9=(-4x)6x -4x-5=0 x= 4 ' 34 = ' 34 6 A= -' A=-' 34 6A=6_{ -' 34 }=-' 34 6 p x -x-=0 x= '5 8 = '5 4 '5 = A ' A==5 4 4 A+=6!0.3x -x-.3=00 3x -0x-3=0(3x-3)(x+)=0 x=: 3 +;3!;x=;6!;6 3x +x-=0(3x-)(x+)=0x=;3!;x=-!@x=- x=- (x+)(x+) (x+)(x+)=-x A (x+)(x+) (x+)(x+)=-x D <x> <x>=a A x 3 <x>=a A x=49 4 <x>=a A x A <x>x <x>=a A D x E 3 (x+)(x+) =(x+)+(x+)-(x+)(x+) =-x -x+ -x -x+=-x +x-=0(x+)(x-)=0 x=-x= 6 p (x+)(x+) (x+)(x+)=-x k=4 36

37 x -4x=k-3x -4x+4=k-3+4 (x-) =k+ (x-) =k+ k+<0 k<- 4 x -3x+a+=0 x +ax+6=0 a p x -0x-m+9=0x -0x=m-9 x -0x+5=m-9+5(x-5) =m+6 (x-5) =m+6 m+6æ0 mæ-3 x= -(-3) " (-3) -4 (a-5) = 3 'ƒ49-8a _ 4 3 'ƒ49-8a a= a356 a=356 a x -3x+a+=0 x +ax+6=0 a 3!x -3x+a+=0 x= -(-3) " (-3) -4 (a+) = 3 'ƒ-8a _ 4-8a>0 +ax+6=0 a= _4= 8a=-4a=4!@a=-4 a=-4 A x -3x+a+=0 D x +ax+6=0 E a F k = k k 3 x +x-k+5=0x +x=k-5 x +x+=k-5+(x+) =k-4 (x+) =k-4 k-4<0 k<4 x +(k-)x+4=0 k-= _= 4k=-3k=5 k=-3 k=-3 4 = k k A = k D E k F 37

38 7 p a3a a+3a=m-m=4a+ 3a =a m=-79 4 a3a k=4 am a amam x -x-4=0 x= '5(+'5)+(-'5)= x -7x+k=0x= 8-4+k=0k=6 k=6 A a3a am D a E amam F p. 4 0 x -6x-=0 x= 3 ' a= 3-' a= 3-' b= 3+' a+b=3ab=-;!; b= 3+' (a<b) ab ab a +b =(a+b) -ab=3 -_{-;!;}=0 a +b =0 0 x -x+k-8=0 a+b=ab=k-8 a +b =(a+b) -ab= -(k-8)=-k+0=4 k=6k=3 k=3 3 a3a am a amam 3 +' -' -a=(+')+(-')a=-4 b=(+')(-')b= a=-4b= x +x-4=0 x +x=4x +x+=4+(x+) =5 x=- '5 4 ab ab 38

39 A ab D ab E a+bab a+babx 3 8 x -6x+8=0 3x +x-=0 x -6x-0=0 p. 44 x +9x+8=0 4x -;6%;x+;6!;=0 3x +8x-48=0 x -5x+=0 a+b=5ab= 3 x -x+3=0 a+b=ab=3 a+b=ab=33 3(x-3)(x-)={x -(3+)x+6}=0 3x -5x+8=0 4 a+bab a+babx 3 A a+bab a+babx 3 D ;a!;;b!;x [x -{;a!;+;b!;}x+;a!;_;b!;]=0 {x - a+b ab x+;a b;}=0 {x -;%;x+;!;}=0 x -5x+=0 p (x-)(x+3)=0x +x-6=0 x +x-6=0 a=b=-6a +b = +(-6) =37 a +b =37 x -6x+=0x -6x=-x -6x+9=-+9 (x-3) =8m=-3n=8-38 (x+3)(x-8)=0x -5x-4=0 x -5x-4=0 3!(x+5)(x+)=0x +6x+5=0 -6x+8=0-6 x -6x+5=0 (x-)(x-5)=0 x=x=5 39

40 4 A D E F 0 x5-x x(5-x)=0x+(5-x)-3-x +5x=9x-6 x -6x-6=0(x+)(x-8)=0 x=8x p x (x-6) x +(x-6) =468x -x+36=468 x -6x-6=0(x+)(x-8)=0x=8(x>6) xx+x+x+3 x +(x+3) =(x+)(x+)+77x +6x+9=x +3x+79 x +3x-70=0(x+0)(x-7)=0x=7x A D E F p h=0 h=05t -5t-00=0 t -t-0=0(t+4)(t-5)=0t=5(t>0) 5 x% x% 40

41 3 x %5000{+;0{0;} x % 5000{+;0{0;}{-;0{0;} 5000{+;0{0;}{-;0{0;}=4550(00+x)(00-x)= x =900x =900x=30(x>0 x=30 p (80-x) m x(80-x)=-x +80x -x +80x -x +80x=600x -40x+300=0 (x-0)(x-30)=0x=0x=30(0<x<40) x=0x=30 4 x% x% A x % x % D E F 0 A : = : A (x+) : x=x : x =x+x -x-=0 x= '5 x= +'5 x= +'5 (x>0) A : DE = : EF 30 5 m x= p. 5 (50-x)(30-x)=344 x -80x+500=344x -80x+56=0 (x-)(x-78)=0x=(0<x<30) m m 3 =xaddef A : DE = : EF : (x-)=x : x(x-)=x -x-=0 x= '5 = +'5 x= +'5 (x>) 4 A : DE = : EF A A :DE = :EF D E 4

42 AD xy ADxy xy A D pq E p+q F 3 x cmy =3x =4y3x=4yy=;4#;x ;4#;x =00x =600x=40(x>0) x=40y=30 (40+30)=40 cm 40 (cm) 4 xy ADxy xy A xy ADxy D xy E F 0 x -3x-p=0 x= -(-3) " (-3) -4 (-p) = 3 'ƒ9+4p _ 9+4p>0!x -=0x +;5!;x-0.=00 p>-;4(; A 3x +x-=0(3x-)(x+)=0x=;3!;x=-!@x=- x=- A D E x -3x-p=0 D p E p x -5x-6=x +x-3x -6x-4=0 x= -(-6) " (-6) -4_3_(-4) = 3 ' _3 3 3 ' 3 p+q=4 = p 'ßq p=3q= 3 x -5x-3=0 x= -(-5) " (-5) -4 (-3) _ a+b= 5+' 37 ab={ 5+' ' 37 =5 ;a!;+;b!;= a+b ab =-;3%; ;a!;+;b!;=-;3%; }{ 5-' 37 }=-: 4 :=-3 = 5 ' 37 4

43 A a+bab D ;a!;+;b!; E 08 xpq96 cm PQx3xx xp Q P =36-3xQ =x PQ=;!;_(36-3x)_x=36x-3x =96 3x -36x+96=0x -x+3=0(x-4)(x-8)=0 x=4x= x 3 3(x-)(x+3)=x +3x-8=0 a=3b=-8ab=-54 ab=-54 A 06-3x 3 ab D ab E!(x+9)(x-)=0x -7x-8=0-7 x -7x-8=0 (x+)(x-9)=0 x=-x=9 A D E F 07 xx+ x(x+)=0x+(x+)-0x +x=x-8 x -9x+8=0(x-3)(x-6)=0x=3x= A D E F A PQx D PQ E F G p. 58 A3 :x=;!;x :;!;x =x = x='(x>0) A D Aa'a A ' aa A3;!;a ' a A4 ' 4 a;!;a A4A ;!;a :'a= : ' :' A A A AA3A4 3 D A4A E 43

44 . A : =:4A y=ax Aa 3 y=ax p. 64 3!(p4) p =4p= : =:4 =4A = A(-34) y=ax (-34)9a=4a=;9$; a=;9$; 3 k=8!y=ax (-8) (3b)b=8 a+b=+8=0 a+b=0 4, A : =:4A y=ax Aa A A : =:4A D y=ax Aa E p !y=ax (b-) -=-3b b =4b=b>0 a+b=-3+=- a+b=- y=ax a<0 y=ax y=-ax x y=4x 3y=ax a D D(pp ) A p D 3 D(pp )p>0 A(-pp )(-p-p )(p-p ) AD =pa =3p AD =A 3p =p3p -p=0p(3p-)=0p=;3@;(p>0) a D(pp )={;3@;;9$;} D{;3@;;9$;} 44

45 4 D(pp ) A p D A D(pp ) A 3 D p E D F 0 y=-;!;x y6 y=-;!;x =6x =, x= '3 x =4'3 A=;!;_4'3_6='3 A='3 AD y=x -4D y=-;!;x +ada A AD 3 y=ax +q 3!y=x -4 p. 68 (0-4)(0-4) y=00=x -4x =4x= x (-0)D(0) +a D(, 0)0=-+aa= k=5 y=-;!;x +(0, )A(0) AD=;!;_A _D =;!;_6_4= y=;#;x ya y=;#;x +a (-3)-3=6+aa=-9 a=-9 p. 70 0!y=ax +q(-5) 5=4a+q +q(4) =6a+q y a=;!;q=3 a=;!;q=3 AD= 4 y=x -4D y=-;!;x +ada A AD A y=ax +qx y=x -4D y=-;!;x +ad a D A E AD F 45

46 PQRS P(p-p +3) RS PS p RS =PS p p P y=x x- y=(x+) y=(x+) (-k)k= k= 3 P(p-p +3)p>0 RS =pps =-p +3RS =PS p=-p +3 p +p-3=0(p+3)(p-)=0p=(p>0) P() P() 4 P(p-p +3) RS PS p RS =PS p p P A P(p-p +3) RS PS p D RS =PS p E p F P G p y=-;3!;x x-4 y=-;3!;(x+4) y=-;3!;(x+4) (k)k=- (0-)-=4aa=-;!; a=-;!;p= xy y=x-3xy p ya 3 33 y=a(x-p) y=x-3x;#;y-3!y=a(x-p) (0-3) p. 7-3=;4(;aa=-;3$; a=-;3$;p=;#; (40) x=4 k=-50 4 y=x-3xy p ya 46

47 A y=x-3xy p D ya E 34 y=a(x-p) +q p. 76 (-5) x=- yoa A OA : O =:3 OA O OA k=5 y=;!;x x y=-;!;x y=-;!;x xy -3 3!y=;4#;(x-p) (p0)a(p0) y=-;!;(x-) -3 y=-;!;(x-) -3{-;K;} ;K;=-: :k=-5 {0;4#;p } #OA : O =:3p : ;4#;p = : 3;4#;p =3p 3p -p=p(p-4)=0, p=4p>0 OA =p=4o =;4#;p = OA=;!;_4_=4 p=4oa=4 p A OA : O = : 3 OA O OA A y A OA :O =:3 D E OA O F OA G 0 0 y=-4x 3-5 (3-5) x=3 x<3 A A(--)(5)(-) A A=;!;_3_7=: : : : 47

48 xya y xa A 3 y=(x+) +4x-5=0(x+5)(x-)=0 x=-5x=a(-50)(0) A(-50)(0)(0-5) A=;!;_6_5=5 4 y=-3x+5k A D y=-3x+5k E A=5 4 y xa A A xy y xa D A E 35 y=-;!;(x+) +3 - y=a(x-p) +q p. 80 y=-3x+5k (-)p=-q= y=a(x+) +(0)=a+a=- a+p+q=(-)+(-)+=0 a+p+q=0 p. 8 3 y=x -xk yk+3 y=(x-k) +k+ (kk+) y=-3x+5(kk+) k+=-3k+5k= k= 0 0 (-)p=q=- y=a(x-) -(0) =4a-a= a+p+q=++(-)= a>0p>0q>0 48

49 y=a(x-) +q (30)()aq 3 y=a(x-) +q!(30)4a+q=0 y a=-q=4 y=-(x-) +4 y=-(x-) +4 4 y=a(x-) +q (30)()aq y=-(x+) + y=-(x+) + 4 y=a(x-p) +q a p q A y=a(x-p) +q a D p E q F G A y=a(x-) +q (30)()aq D E p f()=3_ -5_-= f(-)=3_(-) -5_(-)-= f()+f(-)=_+=3 f()+f(-)=3 xy y=a(x-p) +q a p q 3 y=a(x-p) +q y=x x y=-x y=-x a=- x=-p=- y=-(x+) +q() 4=-8+qq= 0 A f() f(-) D f()+f(-) E x=0y (00) y=-x x 0 x<0xy A D 49

50 D(4p)y=;8!;x p= A(-4)D(4)AD =8 A = =D =;3*;{;3$;} 07 ()p=q= y=a(x-) +(0-) -=4a+a=-;!; y=ax {;3$;}=: 9 :aa=;8(; a=-;!;p=q= a=;8(; A AD D y=ax a +3(-5)5=4a+3a=;!; a=;!;q=3 A yq (-5)a D 08 A pq (0-)a D (4)p=q=4 y=a(x-) +4()3=a+4a=- y=-(x-) +4 y=0-x +x+3=0, x -x-3=0 (x+)(x-3)=0x=-x=3 A(-0)(30)A =4 4 A x pq ()a D y=0x E A F A G 05 y=-x x y=-(x-) y=-(x-) (-k)k=-8 k=-8 A x x (-k)k D 36. y=ax +bx+c p y=;!;(x-) -5 (-5) 3x= A y=(x+) + y=-(x-) + 3y={x-;!;} -;4%; 4y=;!;(x-) -;#; x= (9) 50

51 y =x -8x+=(x -4x+4)-7 =(x-) -7 y=(x-) -7 y=(x-) -7 x=(-7) x=(-7) y=;!;x +ax+b =;!;(x +ax+a )- a +b=;!;(x+a) - a +b {-a- a +b} (-5)={-a- a +b}a=-b=-3 a=-b=-3 p y=x -3x-5={x -;#;x+;ª6;}-: 8ª: ={x-;4#;} -: 8ª: y= {x-;4#;} -: 8ª: y= {x-;4#;} -: 8ª: x=;4#; x<;4#;xy x<;4#; y =5x -0x+=5(x -x+)-4 =5(x-) -4 y=5(x-) -4xy -3 y=5(x-3) -7 y=5(x-3) -7=5x -30x+38a=5b=-30 c=38 a=5b=-30c=38 4 y=a(x-p) +q ab A y=a(x-p) +q y=a(x-p) +q 4 D ab E y=a(x-p) +q y=a(x-p) +q m y=a(x-p) +q y=a(x-p) +q ab 3!y=x -8x+3 y=x -8x+3=(x -4x+4)-5=(x-) -5 +ax+b 3 y=-;!;x +mx-m+3 =-;!;(x -4mx+4m )+m -m+3 =-;!;(x-m) +m -m+3 (mm -m+3) x-y+6=m-(m -m+3)+6=0 -m +5m+3=0m -5m-3=0(m+)(m-3)=0 m=3(m>0) 4 y=a(x-p) +q m 5

52 A y=a(x-p) +q y=a(x-p) +q D E m F y=ax +bx+c f(0)=c f(-)=3f()=-5ab 37 y=ax +bx+c p. 9 3 y=ax #f()=-5a+b+c=-5a+b=-6 a=-b=-4 y=-x -4x+ y=-x -4x+ y=x -5x3 y=-x -x+6 y=a(x+)(x-4) (0-)-=-4aa=3 y=3(x+)(x-4)=3(x -3x-4)=3x -9x- y=3x -9x- p y=ax +bx+c f(0)=c f(-)=3 f()=-5ab A y=ax +bx+c f(0)=c f(-)=3 f()=-5ab D E F 0 y=ax 5=a-b+ca-b=3 y #(-7) -7=a+b+ca+b=-9 y a=-3b=-6 y=-3x -6x+ y=-3x -6x+ y y=ax +bx+c ac b 0 y=a(x+3)(x-) (09)9=-3aa=-3 y =-3(x+3)(x-) =-3(x +x-3) =-3x -6x+9 y=-3x -6x+9 3 y=ax +bx+c a=c=0 y=x +bx+0={x +;;x+ b b }

53 ={x+;4;} - b 8 +0 {-;4;- b 8 +0} y=-;!;x+ {-;4;- b 8 +0} - b 8 +0=;8;+b +b-7=0(b+9)(b-8)=0 b=-9b=8!y=0x +3x-4=0, (x-)(x+4)=0, x=x=-4 x(-40)(, A(-40)(0)(0-4) A=;!;_5_4=0 A=0 ab>0b=8 y=x +8x+0 y=x +8x+0 4 y=ax +bx+c ac b A y=ax +bx+c ac D E F b G H p !y=0x +x-8=0(x-)(x+4)=0 x=x=-4 A(-40)(0)(0-8) A=;!;_6_8=4 A=4!y=-x +8x+4=-(x-) + A()() OA=;!;_4_=4 OA=4 xad y=a(x-p) +qa y=0d AD 38 p. 96 (-6) (-30), (50) A(9)(-0)(40) 3!y=x -x-3 y=x -x-3=(x-) -4 (-4) y=0x -x-3=0(x+)(x-3)=0 x=-x=3 +x-3 y=x +x-3=(x+) -4 53

54 (--4) y=0x +x-3=0(x-)(x+3)=0 x=x=-3 x(-30)(0) A(-4)(--4)(-30)D(-0) AD=_4=8 4 y=a(x-p) +qa y=0d AD A x y=a(x-p) +qa y=0d 4 D AD E A x y=a(x-p) +qa y=0 D A E F 39 p xa a= y=a(x-p) +qa y=0 A (-0)(60)x= 8(8) y=a(x-) +8 (60)6a+8=0a=-;!; 3 y=-;!;(x-) +8=-;!;x +x+6!y=-;!;x -x+6=-;!;(x+) +8 y=-;!;x +x+6 -x+6=0 x +4x-3=0(x+8)(x-4)=0, x=-8x=4 x(-80)(40) A(-8)(-80)(40) A A (9) (-80)(9)y=x+8 y=x+8 4 y=a(x-p) +qa y=0 A p y=3(x -4x+4)-5=3(x-) -5 (-5) (-5) x x=-5-5 x=ky=(x-) +k x +(a-3)x-5=(x-) +k=x -4x+k+4 (a-3)=-4-5=k+4 a=k=-9 54

55 y=a(x-p) +q y=a(x-p) +q M M=k(a-r) +s (-'5) k=-' 4 y=a(x-p) +q k k 3 y=-;!;x +4ax+a=-;!;(x-4a) +8a +a x=4am=8a +a M=8a +a M=8a +a=8 {a+; 6;} -;3 ; a=-; 6;-;3 ; A y=a(x-p) +q y=a(x-p) +q k D k E -;3 ; 4 y=a(x-p) +q M M=k(a-r) +s M A y=a(x-p) +q y=a(x-p) +q M D M=k(a-r) +s E M F 40 5 : : cm p. 45 m y=a(x-p) +q y=a(x-p) +q k k 3 y=-3x +6kx-=-3(x-k) +3k - (k3k -) x=k3k -=5 3k =6k =k= '! k=' ('5) (000+00x)(400-0x) y=(000+00x)(400-0x)=-000x +0000x y=-000x +0000x y=-000x +0000x =-000(x-5) x= x= p yx 30-x y=x(30-x)=-x +30x=-(x-5) +5 55

56 x=5 cm5 cm 5 cm5 cm PQ PQ =a(p-m) +n PQ 0 xm(-x)m y=x(-x)=-x +x y=-x +x y=-x +x=-(x-3) +8 3m8m 3m8m y=a(x-p) +q 3 P(p-4p -)Q(pp+3) PQ =p+3-(-4p -) =4p +p+4 =4{p+;4!;} +: 4 : p=-;4!;pq : 4 : : 4 : 4 PxpPQ PQ PQ =a(p-m) +n PQ 3 (00+x(800-4x) y=(00+x)(800-4x)=-4x +400x y=-4x +400x y=-4x +400x+80000=-4(x-50) x= x= A PxpPQ PQ PQ =a(p-m) +n D PQ E 4 y=a(x-p) +q A y=a(x-p) +q D E PQ PxpPQ p y=-;3!;x +x+ =-;3!;(x -6x+9)+4 =-;3!;(x-3) +4 y=-;3!;(x-3) +4 y=-;3!;(x-3) +4 x=3(34) x=3(34) A y=a(x-p) +q y=a(x-p) +q D E 56

57 0!y=-3x +6x+=-3(x-) +4 05!(0)c= y=-3(x-) xayb =a+b+ca+b= y #(-4) y=-3(x-a-) +b+4 4=a-b+ca-b=3 y=-3x -x-=-3(x+) + a=b=- -a-=b+4=a=-3b=-3 y=x -x+= {x-;4!;} +;8&; a+b=-6 A y=-3x +6x+y=a(x-p) +q D y=-3x -x-y=a(x-p) +q E a, b F a+b G! y=x +ax+b(-) =-a+bb=a+ +ax+a+=(x+a) -a +a+ (-a-a +a+) y=x+5 -a +a+=-a+5a -4a+4=0(a-) =0 a= a=b=5 a+b=7 A y=x +ax+b(-)ba y=a(x-p) +q D a E b F a+b G!y=0-x +4x+5=0 x -4x-5=0(x+)(x-5)=0x=-x=5 A(-0)(50)(05) A=;!;_6_5=5 06 x=;4!;;8&; ;8&; A (0)c ab D y=a(x-p) +q E F y=x +4kx+8k+=(x+k) -k +8k+ x=-k-k +8k+ m=-k +8k+ m=-k +8k+=-(k-) +9 k=9 9 A y=a(x-p) +q 07 y=a(x-p) +q m D m=a(k-r) +s E m F y=-x+4p(ab) b=-a+4p(a-a+4)q(a0) OPQ=;!;_a_(-a+4) =-a +a =-(a-) + a=opq A=5 A xy y=0a x=0 D A E A PQa OPQa D OPQ=k(a-r) +s E OPQ F 57

58 08 yx%00x y=5000{-;0{0;}( x) =( x)( x) h=v=0g=h=-t +0t+ 0 mh=0 0=-t +0t+t -0t-=0t=5+' 7(t>0) (5+' 7) 5+' 7 =-5000x x =-5000(x-0) x= %5000_; 0º0;= A xy D y=a(x-p) +q E F G A D p. 0 y=ax y #(88)8=64a+8b8a+b= y a=-;4!;b=3 y=-;4!;x +3x 0 my=0 0=-;4!;x +3xx -x=0x(x-)=0 x=(x>0) m A y=ax +bx+c (00)c D (5)(88)ab E F G 58

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