!"#"$"%&
& $"% &
'( )
*"+$"% )
* )
,-$"% .
&/0'1 .
23#"4502* , .
-6* , .
3#"450 7
608 7
&" 7
2* 082* 9 :
* 08 :
* 9 :
20*/
2!0!"";
<=>=?@"A?BCBD<ADEFG<H?<BIEJBKLBEMGNB
.
O
&&
<=>=?@"A?PNBGQDKQR= .
<=>=?@MSBTUGVWGA?EX :
<=>=?&@*YGZWCSBTUGG[L?KNVWGA?EX
V€R=PNBGQDEwG<mEF>NUGvSYGZWCk>WiIKNKQR=SBYG<q?
?<[\?<]GS<^?<_<a?VB<>LD>{P*
*<BBCRsi?<[\?<]GS<^>LDGkB<QG<]i<cW<YG?A?lU<a?
VB<EMW]G>uGuS<B>NU?A?PNBGQDKM?<]GS<^PfBEei>ND<c?g<BMW
RsPNBGQDh?g<BMW?kG<q??c<LKNKBI?ADR=?A??kG<q?G_A
<a?G[\EJBD<q?GsDhRr<cU>•_EghS<gS<v>L<]G?b?A?lU>N
KBI?•A?Em<PNBG_AG<WX?RsN_ETE[D<[\D<ADBCBD<ƒ<•D?<_
KBI?BCBPNBG_AEg
_ ZWA Gd< BC Rsih GkB
<QG<]i
<a? VB< G<[n ?<• PBYG >NU
<`PNBGQDE\BCh?t<`PNBGQDixW?cWD<CB?gS<CvD<eG^?<
EM<_o?G[RWih<L>eWKN?<^<•A?SBYG<q?ETKQR=G<d?t<BMW<s?<Y
"A?PNBGQDKMEwG<m?<]GS<^EFE[•?KBYGS<k<BMWWiKQihUXGVJ
?A?GNB>BIWEg?<biYWKBYG?<_<a?VB<S<AKNBŽBGHEa?KN?gG<T<BTWi
K]EMKNADR=KN_?A?PNBGQDS<A?h?tEJBKLBEVJ<a?VB<G<dKBI?GH
<Bx?qW?A?GNB>BIWET‘USBYG<q?>NKk?ƒS<gS<v?<^<h<i<cU
>•SBYG<q?h?<[<BTW’UJB>Bx<IB`?A??kG<q?KNEo?PBIG>N<a?
VB<]GS<g<L
TBuD?<_<a?VB<RrRN‘U E[•?SBYG<q?KNKQR=GJG?A?
D<[\D<AD?\PCBCB?A?PNBG_AG_?A?EMG<BG<WX??<[\?<]GS<^
xGkBEFG<H?<BIEMGNBNi
<H?GYBCRsi<BMWS<g<a?VB<hGkB<QG<]iK]EM?A?lU<a?
VB<<iU‘?D<CB>N<a?GyPNBG<d?g<BTWh<[ET<L?A?SBYG<q?Eg
E[•?>eWKN<BTW’VH>_B?>BxZWB`?A?PNB<a?G<d?A?lU?<[>NUGJG
"<[\?<]GS<^?g?A?D<[\Gd<RBrGCVHPBYEjB?<]GS<^xGkBEF?<u
S<^ G<WX??<[\Gd<>LDe?_
9
|•A?Em<EJBG[•<a?VB<ADR=EMGNB
|d<PNiSBYG<q??\VfVA?<BA_S<_KM?A?Em<>WQGKND<[\Gd<
?<]GS<^
|<[\D<ADVWi>WQGdUSBYG<q?>BxZWEY?A?RsPNBGQDKMEw
G<m?<]GS<^
|[?A?PNBGQDADR=G_GyRsET<a?VB<>WiIGQD
|*BTUGVHGBYDG<W?b<a?VB<P„?A?EMk>WiI
|A<BAhE[VHEBMW?<•<D<[\D<AD?<_D<ƒ<•DGyEJBG[•
<a?VB<
|"<a>LD>NU>LDG<H?<BIUh>LD&>N>LDEJB?<qkBRƒ
EBTUGWPd<Uk<a?Sd|Uk2QG>{>NUPNBSBTUGG[L?GA?EX
*YGZWC?<_G<]iEBTUGWPd<?b<B<gU?gVHS<A?<WhR_Eg
?<uGkBRƒD<‡DSBTU?<q|GlVGETSBTU?<qVH?<x<>I?<GWPd<
KMEBTUVJ?b<B<gUG[L?S<BGA?EX
;<"#=>",*&?@'AB"#$C",.DE$%&0&?@'AE'AFG.'>.*H"#
<gU ŒJŒ BAGmGWPd< X>I?<?<W–ŠŒ4‹ D
<H?<BIU &) 7h h7O IJ26
JBGq &. 7h h:
"<x<>I?<BAGmGWPd<?<W–ŠŒ4‹ IJ2I6
G<]iDˆh&‰h)xVH?<x<>I?<KMEBTUVJGWPd<?b<B
<gU>NS<k?g{<ph<B<gUE[•??_B>NG[\E[\
)
9&?@'AE'AFG.K%EB'>.*H"#KG&",L@'FM"#'FM"#
<gU
*BTUGG[L?
GA?EX
A?EX
*BTUGVW
<H?<BIU JB?<q
BTUGWPd< :h 7h
X>I?<?<W– h: h.7
BAGmD?b|GlVG IJIIIIIIW
"<x<>I?<BAGmGW
Pd<?<W–ŠŒ4‹
JW2
S3TU
.
<[GxEF?<qUB<@SYGZWC<gUG[L?GA?EX>NG[\E[\
ŒWGA?EXSBTU?<q?<x<>I?<EBTUGWPd<P„G|GlVG?<_SYGZWC
Dˆh.•h)ei>NSYGZWC]G?g{<phGq?>NVH?<x<>I?<SYGZWC
EBTUGWPd<<gUG<H?<BIU?_<\<gUEJB?<qS<kD<CBR_
•W<BxUNR_SYGZWC?bGA?EX
BAGmŒ4ˆ
:h 7h
h.7
−
ˆh.G<l_PCGBxW?<^"_<l?<_G<]iUq?EX
C<<[f?bRsi<a??gV€R=GNB>BIWGH<a?EYSYGZWC>N]G>L<[
KQihBCG<WiYG?bEMGNBEFE[•?SBTU?<q
2;X
|BTUGWPd<PNBSBTUGVWGA?EX?b<gUG<H?<BIU>N>N
:h†?b<gUEJB?<q>N7h"<qGŽEBTUGWPd<?b<B>LD?gVH
S<A?<W’IG0LDG<H?<BIU?gEBTU?_<\>LDEJB?<q
|"<x<>I?<BAGmGWPd<?<W–ŠŒ4‹?b<BPNBSBTUG>Nh.
"<qGŽPBID<ADGA?EX?gC<<[f]G>LEYSYGZWC
|<‡DSBTU?<q|GlVGEBTUGWPd<PNBSBTUGVWGA?EX?b
<B>LDKN&>NDˆh.•h)*YGZWCNiS<˜Em<VH
?<x<>I?<EBTUGWPd<?b<B<gUS<kD<CBR_<•<BxUNR_SYG
gDKN_S<_D<[\D<ADBCBPNBGQDKQG>{<iKN?g<BIWZWC
9Y
BA_KBxG<[n•WixGH<a?hGHPwBR[™ETe?_Gd<EX?<Wix
Uk4si<a?SYG<•DV€R=D<[\D<ADEwG<mETGs_?<_<a?VB<G<gBZWl
<B<LKN>NUEuPNBGQD?<[\?<]GS<^
MGNBEFE[•?G<€<BIUfG[nD<jG<kh•_KBI?ADR=?tf
UXGD<sUKB<šD4_KQihETEMGNBE[•?SBTU<BIUKNU>sB<BIWZWC
G<BYGG<H?<\?cE[•?G<€<BIUGxUXGD<sUKBX<\h
o?RƒEF?J‘]G<BMWKNEMGNB?}EFEsGE[•?<`SYGZWC
<]GEm<h•_?<‘??<‘S<kGA<S<ŽB<`G<BYW•gGhGA?BC]GU_
:
<QE[•?<`{SBYEggD?b?A?G<ci?kG_GjKQG>{G[n
xm<gBBxKN?A?PsEw<BIDgB?<W
Xin trân trọng cảm ơn!
Thanh Hóa, ngày 16 tháng 05 năm 2013
Z>.",(".DE',D'AF["#*M"K- #F\&K&]'
kB•B?UE_Eei>N"*Œ'4
?bUd<KBYGhS<kV_?<‡D
XBRW?b[nBS<A?
#B^_"R`"F\"#
R9P
O
2QG0^e?_|Wir<Y*<kBh<sU,W{[h0xa[nh
0[\]GsGh0x"<eƒhWira?[h<sUd<<BYGh6ƒB
aWe|ŒA?<BA_S<_<N•W]GPC4|.
6NBGQDKQG>^e?_|0xa[nh0[\]GsGh0x"<eƒh
<sUd<<BYGh6ƒBaWe|<N•W]GPC4|.
BCBG_A2QG>^|QD|6ƒB,Wehc2v6wBh<sUa?BYh
Wir<N<[\|<N•W]GPC4|OOO
T
ˆ?_VG
• YWPBTWRBrG_<IŠh‹<_o?Šh2‹ →RƒRsŠ<d<hP‹
• YWPBTWRBrG_<IŠ2h‹ →RƒRsŠ<d<?‹
hçnh 1
2
2
hçnh 2
2
2
hçnh 3
2
n,&",G0&]"',o.V
—•BE˜ZWAGd<GxW?CRsD<[\Gd<G<dULBRBrGCEci
EbVHG<iEjBG<kVJGsG<ABDh2h
—6CGj<•D<d<RsEwG<mKN?A?D<[\Gd<G[\q@
m<>WQG
6kB|>\|U|B|JG
m<>WQG
ŒA?|0\
m<>WQG
i|0Wi|•‘?
,WAGd<E˜<BIG ,WAGd<E˜G^?< ,WAGd<E˜AD
2ˆ?_VG Dˆ?_VG
2
2
2
2
ˆ?_VG
_VG
_VG 2G G
p c
V
c
T
=
= → →
,WAGd<RFE˜<BIG|@
_VG
_VG 2G BU
T c
pV c p
=
= → →
,WAGd<‡E˜AD|&@
2
)
r)
)
)
R
/
D
/
2
/
2
D
/
D
2
/
D
/
2
_VG
?<]GS<^G_<IŠ2h‹KNŠh2‹
FG"# q"
žZWAGd<|@2ˆ?_VG@E˜G^?<
Gv @ →WgE˜G^?<
Gv @Wg
žZWAGd<|@ˆ?_VG@E˜<BIG
BCU @ →BFfE˜<BIG
2Gv @BFf
žZWAGd<|@ˆ?_VG@E˜AD
BCU @>NU>s< →>NU>s<E˜AD
2BCU @‡ →‡E˜AD
P"<WiTV<IŠ2h‹KNŠh2‹
ž,WAGd<|@
›4s@2ˆ?_VG
›4s@Dˆ?_VG ŠDG•>IG<WQKLB‹
ŠGvhGv‹
,WAGd<|@
›4s@ˆ?_VG
›4s@D2ˆ?_VG ŠDG•>I<m?<KLB2‹
ŠDBCUh2Gv‹
&
2
Šh2h‹ˆ
pV
T
ˆ"
ŠD<[\Gd<GsG<AB‹
*<€G_G<kVJGy<IGxGE[•?UXGD<[\Gd<>Bx<IB`
<BG<kVJ?t>sB@<Ših•‹ˆ"
<iiˆŸŠ•‹
›;FG.2@*<C_VAG<NUVJiˆŸŠ•‹GK‚E[•?EwG<mG_<IŠih•‹
•∈ h2h¡
i∈ h2h¡h•≠i
• YWPBTWRBrG_<IŠh‹G<dGS<€G<kVJ2
• YWPBTWRBrG_<IŠh2‹G<dGS<€G<kVJ
• YWPBTWRBrG_<IŠ2h‹G<dGS<€G<kVJ
) !"##&<&.>. p"#'=>"
;%&'=>"K1 !V
"<_PBYGUXG>[•S<^PBYEjBG<l_
UXGZWAGd<<[EwG<mPx
FiPBTWRBrZWAGd<PBYEjB?b
?<]GS<^G_?A?<IŠh‹KNŠh2‹
FG"# q"
|<Q•‡G@,WAGd<|S<kD<CB>N?A?E˜ZWAGd<
→S<kG<TV€R=E[•??A?D<[\D<ADG<kG<[n
|yEwG<mhG?gZWi>WQGPBYEjB?b?<]GS<^@
ˆ2 ŠˆGα@>N<IVJg?‹ Š‹
¢
|<[\Gd<GsG<ABS<^>^G[f@
pV
‹2
→ˆ"
2
>N<NUPQ?<B?b2xEwG<m>NUXGD<c?bDP_>Š<d<K‚‹
*Ghi nhớ kiến thức : Hệ số C
1
≠
C
2
nên độ cong đồ thị là khác nhau.
;%&'=>"K1 !V
"<_PBYGUXG>[•S<^PBYEjBG<l_UXG
ZWAGd<<[EwG<mGxFiPBTWRBrZWAGd<PBY
EjB?b?<]GS<^G_?A?<IŠh‹KNŠh2‹
FG"# q"
ž,WAGd<|@
›4s@2ˆ?_VG
›4s@ˆ?_VG ŠGvhGv‹
ž,WAGd<|@
›4s@ˆ?_VG
›4s@2ˆ?_VG ŠBCUh2Gv‹
ž,WAGd<|@ˆ2
Š‹→ˆ"
2
2
2
><?gD^GGkS^wB?<_>[•S<^<l>BEg
PBYEjB?<QU?<sDGyGsG<AB?gG<TG^?<
2
ˆ>BGh
ˆ&hGUVGsG<AB?g
G<TG^?<2
ˆO>BGh
ˆ)h)GUŽB<BIGEX>L<]GUNS<^EsGE[•?>NP_
<BxW£?<_PBYGZWAGd<PBYEjB?b?<]GS<^<[<d<K‚
FG"# q"
DVW]G>N<NUPQ?<]G?bG<TG^?<2
b−
ˆ>
ADVW]G@
U•
ˆ2
U•
›PˆGU
2Qi
U•
ˆ
U•
2
U•
m
µ
ˆ&O*
2M[bk',B^]'V <[\Gd<GsG<AB?bS<^>^G[f@
pV
T
ˆ?_VG
:
2
2
ˆ
2
a
YW
‰
→
‰
→EwG<m
fGx
Š<d<K‚‹
2NB>'AC",*h"#'1., @ ˆ
_VG
2
c
›,WAGd<E˜G^?<2
@
ˆ
_VG
2
c
c
›,WAGd<E˜AD
@
2ˆ
_VG
D
c
ˆ?
›,WAGd<E˜AD
@
2ˆ
_VG
D
c
ˆ?
YW
‰
→?
2
2
2
2
FG"# q"
>.,@Œ€R=RsD<[\Gd<G_A<a?
<[\Gd<GsG<AB@
pV
T
ˆ?_VG →ˆ
_VG
2
T c
ˆ
2
→
?_VG‰
?_VG
→
‰
ŠED?U‹
>.,@
|2‚E[nE˜G^?<?‘G<BE[nE˜<BIGGsBKNŠ<d<K‚‹*<B
EghG?g@
p T
p T
=
•ŠKdK•
‹ →
•
ŠED?U‹
2;%&'=>"K1 !V
d<PxPBTWRBrE[n
E˜G^?<?bUXG>[•S<^q
KLB?A?G<TG^?<2
@ˆ
_VG
2
c
ˆP
2dE[n2
fGx2
→P
‰P
→
_VG
2
c
‰
_VG
2
c
→2
‰2
wG<m<d<PxUkGCUXG?<WGd<?bS<^>^G[f
Fi?<•Gx?<WGd<@
|"A?EBTU?bEwG<mqKLBADVW]G>L<]Gh<Ž<]G
|"A?E_s?bEwG<mqKLBADVW]GGvhBCU<_o?S<kEjB
FG"# q"
|•‡GUXGEBTUP]GS…GxEwG<mhK‚E[nE˜AD/Š
‹
IVJg?E[nG<˜/>N@G
M
α
ˆ
M
M
V
T
|yD<[\Gd<GsG<AB?bS<^>^G[fh
?g@
M M
M
p V
T
ˆ?_VG
→
ˆ
_VG
2
α
6
≤
G
α
≤
G
α
→
6
≥
≥
→
U•
ˆ
6
h
UB
ˆ
µ
FG"# q"
y
K‚E[nG<˜V_V_/2h?‘G/
µ
h
/
µ
>c>[•GGsBKN6
DR=D<[\Gd<?>|Dx|k|l|Ex|>x|‡DGsBKmG^KN6@
/
2
µ
µ
6
2
2
µ
µ
=
→
=
V
V
µ
µ µ
µ
= > → >
2x;%&'=>"K1 !x V
XG•i><?<qS<^Pm<fxS<^?gG<T<_o?
KN_•i><?<QU*<BADVW]GDS<kEjBhG<TG^?<
2PBYG<BxG<l_<[EwG<m<d<K‚ŽB>[•
S<^G_•i><Gv<iBCU
FG"# q"
y
6&<&),>)6V
t !"#*+',-=>",.u"#K%",&e'.,/'0,1'AE=*j&
'A="#.>.iB>'AC",$&]"*j&'Ap"#',>&
/
2
/
2
6
2
2
6M[bk',B^]'V
6BTWG<q?Wix>{0@
U A Q∆ = +
h
Š ‹A A A p V= − = − ∆ = − ∆
∑ ∑
Š ‹U f T=
*<BE\KmŠD‹h2ŠU
M
A p V V R T T R T T
ν
µ
= − = − = −
• X>L?k@
A =
4BIG^?<2
2
• 6BTWG<q?Wix>{0@
U A Q∆ = +
6 AÏp !"##&<&.>. p"#'=>"
6;%&'=>"K1 !VXG>[•S<^E[•?RFGyG<TG^?<2
EYG<TG^?<2
Š2
‰2
‹Œ_VA<?kS<^G<H?<BIG_?A?ZWAGd<@
‹˜AD
P‹˜<BIG
?‹4FE˜ADwBE˜<BIG
R‹4FE˜<BIGwBE˜AD
FG"# q"
ˆD
2
2
2
2
2
2
2
2
2
XG>[•S<^>^G[fS<kEjBfGsG<AB?gG<TG^?<2
hADVW]GD
h
RFE˜<BIGEYGsG<AB?gG<TG^?<2
ˆ2
ŒWEgRFE˜ADV
GsG<AB?gG<TG^?<2
ˆ2
‹2‚EwG<mPBTWRBr?A?ZWAGd<GxG_<ID|2
P‹4ƒEwG<mETV_VA<?k?bS<^G_?A?ZWAGd<Gx
?‹2QR=Wix>^0D<eG^?<VHG<iEjB?bXBvKN
<BIG>[•?<]GS<^G_EjBKLBUkBG[n_NB
FG"# q"
‹2‚EwG<m
P‹"v?qRBIG^?<?A?<d<hG?g
‰
?‹ž•‡GZWAGd<E˜<BIG|@
T T U U U= → = → ∆ =
2
→
‰
→
U∆ >
@XBv?<]GS<^Gv
<l_Wix>{0@
U A Q Q A U∆ = + → = − + ∆ >
@
Š?<]GS<^<Q<BIG>[•GyPx_NB‹
62;%&'=>"K1 !2V
"gh&U_>?<]GS<^>^G[ff<BIGEX*
WgS<^E˜ADEY<BIGEX)*h<BIG>[•
?W?]D?<_S<^G_ZWAGd<Ai>N>N¦ŒW
EgS<^E[•?>NU>s<E˜G^?<EY<BIGEXP„<IG
&
2
2
2
2
2
D
P‹^<?k
h
A
S<^G<H?<BIG_ZWAGd<E˜AD
h
Š ‹ Š ‹ Š ‹
M
A p V V R T T R T T
ν
µ
= − = − = −
ˆh&:hŠ)|‹ˆ):h7Ц‹
?‹^<EXPBYG<BxXBv?bS<^fU•BZWAGd<?b?<WGd<
DR=Wix>{0@
h
U A Q A Q∆ = + = − +
Šˆ|
h
A
‹
žXPBYG<BxXBvG_ZWAGd<E˜AD@
h
U A Q A Q∆ = + = − +
ˆ|):h7›ˆ&:hЦ‹
Š ‹ Š ‹U f T f T∆ = − =
&:hЦ‹
;%&'()K(" !"#V
d<Px>NEwG<mPBTWRBr?A?ZWAGd<PBYEjBGsG<AB?bUXG
>[•S<^G_<IŠh2‹Fi@
)
2