第二十一章 二次函数与反比例函数·拔尖卷
Ⅰ
!"#$ 10 '()* 30 *(,' 3 *-
1 #3 *-./01 = ()
23401(56 m 7892# -
A 0
B 3
C 0 : 3
D 1 : 2
A
*;<=340179>?@34AB7CD(EFGH340179>2I JK
L340179>MN + 2 = 2(O 0(P@34ABQMN
R
01 = ()
23401(
+ 2 = 2(O 0(
N = 0: = 3#ST-(
U!
A
2 #3 *-#24-25 VWXY·Z[Z\·]^-_`3401 =
+ (abc <
2def
7ghijk
(lm (n7o8de2# -
A 1 < < 2
B 1 2
C 1 < 2
D 1 < 2
D
*;pq<=34017rst17t(uqEFGHvwxyzD34017{|
2I }Lh(~ =
+ = (
) +(MN7b2
= (
(U
> u(y x 7(
bc <
2def7ghijk x(lm (
2 × 2 + (P <
2(MN
R
=
+ = (
) +(
7b2
=
(
> u(y x 7
bc <
2def7ghijk x(lm (
2 × 2 + (
1(
< 2(
1 < 2(
U!
D
3 #3 *-#24-25 WX··]^-.r(01 =
+ 1 = (
)#21(O
0- ¡tf7rsMw2# -
A
B
C
D
B
*;<=4013401rs7¢£¤(EFGH401¥34017rs{|2
7I *¦b§!¨©34017A?b¥401ª«¬7s®*(QM£¤
RA?3401 =
+ 17rs( > 0(n401 = (
)7rs«¬?¯?
°s(U!¨ A ±²³
bc B(C(D(~401 = (
)7rsMN > 0(n3401 =
+ 17rsC(
b2
=
=
1
> 0(C y ´µ(U B !¨¶·(C(D !¨±²
U! B
4 #3 *-#24-25 VWXY·¸¹º\·»¼F½-¾¿À01 =
7rsm( !"),!#( !),!$( !)
¯Á(# -
A a" < 0(n" >
B a" > 0(n" >
C a" > 0(n|"| < ||
D a" < 0(n|"| < ||
B
*;<=¾¿À01rsÁ7 ¡ÂÃ(KL¾¿À01rsÁ7 ¡ÂÃQM E
FGH¾¿À017rsÂÃ2I
R
*¦ÄÁ ")(# )($ )ÅÆÇN
" =
( =
( =
(
" =
( =
&(
a" < 0(n
< 0(
" < < 0(
|"| > ||(
A(D ȱ²³
a" > 0(n
> 0(
" > > 0(
|"| > ||(
B ¶·(C ±²
U!
B
5 #3 *-#24-25 WXY·ÉÊËÌÍ·»¼F½-.rªÎ( ¡t©mÏÐ(ÑÒ
7ÓÁ#('l
(®c
7ÏÐÔÕc((($()°Á(a( = 2($( = 3(
$) = 5(n#'7Öר# -
A 4
B
9
2
C 3
D
7
2
D
*;pq<©Á ¡Ç(EFGH©ÁÇ27I Ù-7Öר(n
. = (
/
= + 2(
0 = + 5(
1 = + 10(ÚÛ
2 =
1
2(
. +
0) = +
5
2(
3 =
1
2(
/ +
1) = + 6(QMNÜ
R
Ù®c
7ÕcÁ-
Ù-7Öר(n
. = (
/ = + 2(
0 = + 5(
1 = + 10
~©ÁÇMN
2 =
1
2(
. +
0) = +
5
2(
3 =
1
2(
/ +
1) = + 6
#' =
3
2 = &
5
2 =
7
2
U!
D
6 #3 *-#24-25 VWXY·ÝÞ·]^-.r(ßà4#$7ÓÁ
¶á(4 = 6(¾¿À
01 =
> 0)7rs¬Á$ßà7b©â5(n78Ø# -
A 8
B 8 2
C 4
D 4 2
B
*;<72ßà7{|(ãä9å7CD(¾¿À017{|(EFGHÑÒ7{|27
I³
Jæç5 = $5(4$ = 4 = #$ = # = 6(Ù$(
)(MN5
6
2 ,
2 (
=
6
2 8
2(Ú
= 2(¬$è
$9 : 4c9(PéÚQM
R
ßà4#$7ÓÁ
¶á(4 = 6(
5 = $5(4$ = 4 = #$ = # = 6(
(6,0)(
Ù$(
)(
5
6
2 ,
2 (
=
6
2 8
2(
N
= 2(
¬$è$9 : 4c9(
49 = 2(
$9 =
62 = 4 2(
$ 2,4 2 (
= 2 × 4 2 = 8 2³
U!
B
7 #3 *-#2025·ÉÊ·êëìí-îïmðñ“òó”7ôõ¨ö(÷øå2ù¬úû7ü×ýþúÿ
Āā(úÿĀā7jĂăüĀĄ©Āą7jĂ(Āą; ; =
<
= ĆÜ918(; 22A)u('ÌĆćĈĉ
ĊÛċČ(; < 22AuċČčÌĎď(;ĐuĊÛ7ċČĐđ r 1 ØîĒúû7ü×(> dB)u
ē(A s)jĂ7tr(r 2 ØúÿĀā7ā8(= C)úû7ü×>jĂ7tr#¾¿À01rs7Ĕ
*-(_`'ÌĆÏĕ7ĀĖ<Ø220V(YėĘę±²72# -
A 4su(úÿĀā7ā8Ø
20
3 C
B 2sućĚěċČ
C 3Ĝ6suĊÛ7ċČĐđ
D ĊÛċČ7uÖĝ¬5s
D
*;<4017CD(¾¿À017CD(Ğ9t1ę·9017Ç(01rsÁ7
¡ÂÃğ`ĠÁ(¶·åhv·901Ç27I ~r 1 MN(0~3su(017
ÇØ> = *A³3~6su(Ù017ÇØ> = 75³6~7.5su(Ù017ÇØ> = *A + 375³~
r 2 MN(÷rsØ01= =
500
> 7Ĕ* Lġ}4b§!¨®*QMèÛ£¤
R
.r 1(
0~3su(Ù017ÇØ> = "A(¬Á(3,75)(
3" = 75(N
" = 25(
0~3su(017ÇØ> = *A³
3~6su(Ù017ÇØ> = 75³
6~7.5su(Ù017ÇØ> = A + G(¬Á(6,75)((7.5,0)(
6 + G = 75
7.5 + G = 0
(N
= *
G = 375
(
6~7.5su(Ù017ÇØ> = *A + 375³
.r 2(ÙĢrs701ÇØ= =
> (¬Á(10,50)(
50 =
10(N
= 500(
ÙĢrs701ÇØ= =
500
> (
A 4su(> = 75(
Ä> = 75ÅÆ= =
500
> (
N
= =
500
75 =
20
3 (Uġ!¨¶·³
B ÄA = 2ÅÆ> = *A(N> = 50(
= =
500
> =
500
50 = 10(
; =
<
= =
220
10 = 22(ćĚěċČ(Uġ!¨¶·³
C ~r 1 M`(3~6su(>Đ(
~01t= =
500
> M`(ġu=Đ'(
~01t; =
<
=M`(ġu;Đ(
ĊÛ7ċČĐđ Uġ!¨¶·³
D ; = 22u(= =
<
; =
220
22 = 10(
ġu> =
500
= =
500
10 = 50(
Ä> = 50ÅÆ> = *A + 375(
N
50 = *A + 375(N
A = 6.5(
Ä> = 50ÅÆ> = *A(
N
50 = *A(N
A = 2(
ĊÛċČ7uÖØ&F* = 4.5(s)(Uġ!¨±²
U!
D
8 #3 *-#2025·ÉģĤĥ·êëìí-.r($"H =
7
(0
4)
ÕcÁ4 "(Ä
$"´}4ĦÏ4(*¦NÜ$,$(
ÕcÁ",,( = 7 < < 0)ħ 3 Ð
7 6 ĨÕÁ7ĩ ¡Ī2# -
A 18
B 20
C 36
D 24
C
*;pq<=34017Ħī(KLĦNÛ3401tÇ(27I JÚÛ"
7 ¡"(4,0)(NÛ$"´,4Ħ7ĬĭØ 4(KL3401ØĮuÏĨK7tQM
R
Ä = 0ÅÆ$"H =
7
(0
4)(
N
= 0:
= 4(Q"(4,0)(
U$"´,4ĦĬĭØ 4(
Ù#"(#(#(#I(#J(#K7ĩ ¡*¦Ø
"(
(
(
I(
J(
K(
#"(#u$" = (7 < < 0)(
Q#"(#7ĩ ¡Ø
7
= 07K(
" +
=
G
=
7
1 = 4(
+
I =
" +4 +
+4 = 12(
J +
K =
+4 +
I +4 =
" +4 + 4 +
+4 + 4 = 20(
= (7 < < 0)ħ 3 Ð7 6 ĨÕÁ7ĩ ¡Ī = 36
U! C
9 #3 *-#2025·ÉģįÞ·¯ê-.r( ¡tfm¶İıà#$(')($(2,1)(((4,1)(a
=
( 0)7rsIJN¶İıà7İĨÓÁ*ijÑ7ϵ(,µ§¯ĨÁ(n7Ĵ187Ĩ1Ø# -
A 2
B 3
C 4
D 5
C
*JÚN¶İıà7ıÖ(Pù¬¶İıà7fÚNL#$(ĵĶ$(è#9 : $c9(ù¬ğ
ķ¯à¯ãä9å(ÚN$(ĸÎÛÁ7 ¡( =
( 0)¬Á((4,1)u( = 4 × 1 = 4³
=
( 0)¬Á 2,1 + 2 3 u( = 2 × (1 + 2 3) = 4 3 +2 < 9(ĹÛ4 < < 9(ĺĻNÜ7
Ĵ187Ĩ1
R
$(2,1) ((4,1)(
$( = 7 = 2(
ļıà#$(')2¶İıà(
# = #$ = $( = 2(÷fØ& × 180° = 720°(
L#$ =
720°
6
= 120°(
ĵĶ$(è#9 : $c9(.rªÎ
# = #$(L#$ = 120°(#9 : $(
L#9 =
L#$
2
= 60°(9 = $9(
L#9 = 30°(
#9 =
1
2# = 1(
9 =
##9 =
21 =
3(
$ = 9 + $9 =
3 +
3 = 2 3(
2,1 + 2 3
=
( 0)¬Á((4,1)u( = 4 × 1 = 4³
=
( 0)¬Á 2,1 + 2 3 u( = 2 × (1 + 2 3) = 4 3 +2 < 9³
4 < < 9(
nMo 5(6(7(8($ 4 ĨĴ18(
U!
C
ÁĽ;pq<=¶İıà7{|?Á7 ¡¼Ö×7t?¾¿À01t17{|?ãä9
å?ğķ¯à¯(EFGH`ĠÁ27I
10 #3 *-#24-25 WX·ľĿ\·]©- =
+G
+ N 0)7bØ
= (÷
Ĕ*rsÕ x ŀácÁ A(Õ y ¶ácÁ B(.rªÎ(nYėŁ
①G7N > 0³
②G = 0³
③ + G G#m Øghł1-³
④Á
7
2 ," (
3
2 , (
5
4 , 2Ģ7Á(O" < <
÷©¶·7m# -
A ①②③
B ①②④
C ①③④
D ①②③④
A
*;<rs3401t1Īē7t ~7rs x m 2 ĨÕÁ(}LK7£¦Ç
M`G7N 0 7t(M£¤①³KLbĹå a?b t(M£¤②³KL
= u(m
Đ8(QNÛbcghł1 m ÈmG + N +G + N(M£¤③³KL7ŃńŅ(£¤
0187'(M£¤④
R
①rs x m 2 ĨÕÁ(}LK7£¦ÇM`G7N > 0(¶·³
②7bØ
= (Q
G
= (
G = 0(¶·³
③rsY(bØ
= (
= u( = G + NmĐ8(bcghł1 m ÈmG + N +G + N(QG ( + G)(
¶·³
④
5
4 , 7bÁØ
13
4 , (
7
2 <
13
4 <
3
2(
> > "(±²³
U!
A
3 ņŇ#$ 6 '()* 18 *(,' 3 *-
11 #3 *-#23-24 WX·¸¹·]©-3401 =
+G
+ N7018ijk
Īē7Ĕ*bC8
.ĸ
ġ01rs7A2
(ņ“”:“Y”)³
= 5u( =
……
0
1
4
……
……
4
7
……
4
*;<=34017{|?3401rsÁ7 ¡ÂÃ(uqEFGHvå2I }
Lh(KL7b{(
= 0?
= 4u7018Ôğ(ĺĻėÇŊŋQMN
R
~hN(
= 0?
= 4u7018l2Ôğ(
ġ01rs7bØ
=
04
2 = 2(Q
= 2
< 2u(
7Ō'(
7b2
= 2(
= u
= 5u7018Ôğ
= u( = 4(
= 5u( = 4
UØ
(4
12 #3 *-#24-25 VWXY·Z[ó\·]^-.r(_` l y ?x *¦Õc A?B ÏÁ(¾
¿À01 =
8 2
(
< 0)7rsÕc C?D ÏÁ a C?D ÏÁؼ#7¯ğ*Á(ĵĶ4$?4((n P 4$(
ōØ
6 2
*;<=¾¿À01Ŏŏ¢(~hMN$Ø(7©Á(QP.R0 = QP0R/(Ù$
8 2
(
( S)(~©Á ¡ÇMN((
16 2
S (ÅÆ¾¿À017ÇMNS =
3
2(è$9 : c9(
n$9 =
8 2
(4 = S =
3
2(P~¯àōÇŊŋQMN(EFGH`ĠÁvxyzD2ġ
7I
R
C?D ÏÁؼ#7¯ğ*Á(
$ = $( = #((Q$Ø(7©Á(
QP.R0 = QP0R/(
Ù$
8 2
(( S)(
~©Á ¡ÇMN((
16 2
S (
ÅÆ¾¿À01ÇMN
16 2
× (S) = 6 2(
S =
3
2(
.r(è$9 : c9(
n$9 =
8 2
(4 = S =
3
2(
QP.R0 =
1
24 8 $9 =
1
2 ×
3
2 ×
8 2
= 6 2(
P 4$(ōØ6 2(
UØ
6 2
13 #3 *-#2025·ŐőŒ\·¯ê-_` =
7
+ 27bØ
= 2
#1-78Ø
#2-a =
7
+ 2YĦ > 0)ĨœŔÖ×Ļ( <
< 4def
ŕmĨÕÁ(
n7o8de2
1
2 < 7
*;<=34017rs{|(34017Ħ(GH`ĠÁ7CD27I
#1-~hM`
7
= 2(ÚÛ78QM³
#2-~hM`ĦĻ01ÇØ =
7
+ (ĺĻù¬34017Ħ(34017{|QM
Ú
R#1-~hM`
7
= 2(
N = 1(
UØ
1³
#2-~hM`ĦĻ01ÇØ =
7
+ (
ÓÁ
u((7)7 × 1 × () = 0(
N = (QŖĦ2ĨœŔÖ×(ŗŘÐř³
~cc
= 2b(
0 <
< 4fb(
aŚÕÁ(ćśmÏĨÕÁ(aŕmĨÕÁ(n
ÕÁŕw <
0(
U
= 0u( = 0(N 2(
= u( = ()7 × () + = , > 0(N < 7(
7o8de22 < 7(
UØ
2 < 7
14 #3 *-#24-25 WX·¸¹Ŝŝ·]^-.r(Şş7şŠMšŢţŤť(÷ÇØ
=
1
2
+2(ŦqbħŧŞş®Ũũ(ŪūuŐŬŭŮců7ŰűŲ(qÚÔųŰűŲĪē7Ĭ
ĭØ0.3m(ŴĐıŵ7ŰűŲÜşŠŶĔ77ĬĭMŗc0.3m(Qr©U 0.3m(#V 0.3m(nĐ
ļMŐŬŰűŲ
Ð
14
*;<34017CD(I2ŷD1à7ŸŹ
ź = 0(ÚÛ
78(ĺĻłŻńŅNÛŁ
R
ź = 0(n
1
2
+2 = 0(
N
= 2:
= (
# = 4(
ÔųŰűŲĪē7ĬĭØ0.3m(U 0.3m(#V 0.3m(
´µ
= 0.15(0.45(0.75(1.05(1.35(1.65,1.95($ 7 Ð(
åżµĐļŐŬ 7 Ð(
ĐļMŐŬŰűŲ 14 Ð(
UØ
14
15 #3 *-#2025·¹Žžſ·¯ê- ¡t
4©( =
ƀƁ =
< ÔÕc
5(WÏÁ(÷©Á53s Ù$( )ØƀƁ =
< Á($5($W*¦Õc'(
)ÏÁ(n4'4) 78Ø
4
*;<¾¿À014017¢(GH3Ƃ7ƃ;{|2Ƅ;7I Ù5( )
nW( )(*¦ĸÎÛ5$(W$7Ç(ź
= 0MŊŋÛ4'4)7Ö(ÔŌQMNÜŁ
R
Ù5( )nW( )(
Ù5$7ÇØ
= S
+ G(ÅÆ$( )(5( )
n
S + G =
S + G = 2
(
N
S = 2
G =
(
5$7ÇØ
=
2
(
4' =
(
ÙW$7ÇØ
= X
+ A(ÅÆ$( )(W( )
n
X + A =
X + A = 2
(
N
X =
A =
(
W$7ÇØ
=
+
(
4) =
(
8 () = (
= (
4'4) =
+
= () +
+ () +
= + + 2
= 4(
UØ
4
16 #3 *-#23-24 WX·¸¹ƅƆ·]^-3401 =
+G
+ N G NØ1(OG 0)«¬
(1,0),(
",0)(401 = ||
+ N«¬(
,0)(401 = |G|
+ N«¬(
,0) _`* <
" < 7 <
< + 1(S <
< S + 1(÷© SØĴ1(n + S78Ø
,: 5/5 :,
*;pq<=3401401¢ KL3401b7{|(401 ¡7Õ
Á ¡ėÇŊŋQM
RY3401 =
+G
+ N G NØ1(OG 0)«¬(1,0),(
",0)(
+ G + N = 0(
G
=
1
"
2
=
1
2 +
"
2 (
* <
" < 7(
<
G
=
1
2 +
"
2 <
3
2(
7 <
G
< (
3 <
G
< 4(
1
4 <
G <
1
3(
401 = ||
+ N«¬(
,0)(401 = |G|
+ N«¬(
,0)
=
N
||(
=
N
|G|(
> G > 0u(
=
N
|| =
N
=
G
= 1 +
G
(
=
N
|G| =
N
G =
G
G
=
G +1(
4 <
= 1 +
G
< 5(
5
4 <
=
G +1 <
4
3(
<
< + 1(S <
< S + 1( SØĴ1(
= 4, S = 1(
ġu + S = 5³
< G < 0u(3 <
G
< 4(
1
4 <
G <
1
3(
=
N
|| =
N
=
G
=
G
(
=
N
|G| =
N
G =
G
G
=
G(
* <
=
G
< 7(
4
3 <
=
G <
5
4(
<
< + 1(S <
< S + 1( SØĴ1(
= * S = (
ġu + S = ,³
UØ
,: 5
Ⅱ
¯ #$ 8 '()* 72 *-
17 #6 *-#24-25 VWXY·¸¹ƉƊ·]^- ¡t©(¾¿À01" =
"
#"Ø1(" 0-
7rs401 =
+ G#(GØ1( 0-7rsÕcÁ(2,3)(#( )
(1)Ú m 784017ĸĆdz
(2)" > u(ĶƋÛ x 7o8de³
(3)aÁ5( G)ÁW(N X)01"7rs(O + N = 6(ÙU =
1
G
1
X(1 < < N < 5u(Ú P 7o8d
e
(1) = ( =
+ 1
(2)
< :0 <
< 2³
(3)
2
3 < U < 0
*;<=¾¿À01401¢(EFGH¾¿À014017{|2ġ7I
#1-ŷDĞ9t1ęÚQM³
#2-~01rsQMN³
#3-~hMNG =
6
(X =
6
N(~ + N = 6NN = &(ĸÎÛU =
1
G
1
X =
3 (1 < < N < 5(Ŋŋ
QMN
R#1-
ÄÁ A ¡Åƾ¿À01ĸĆÇN
" = 2 × 3 = 6(
ª¾¿À017ĸĆÇØ" =
6
ÄÁ B ¡Åƾ¿À01ĸĆÇN
= (
ªÁ B 7 ¡Ø( )
Ä A(B ÏÁ ¡ÅÆ401ĸĆÇN
2 + G = 3
+ G =
(
N = 1
G = 1
(
ª4017ĸĆÇØ =
+ 1³
#2-
~01rsM`(" > u(x 7o8de2
< :0 <
< 2³
#3-
Á5( G)ÁW(N X)01"7rs(
G =
6
(X =
6
N(
~ + N = 6N
N = &(
U =
1
G
1
X =
6
N
6 =
N
6 =
(&)
6
=
3 (
1 < < N < 5(
1 < < & < 5(
1 < < 3(
2
3 < U < 0(
P 7o8deØ
2
3 < U < 0
18 #6 *-#2025·ƌƍƍŐ·êëìí- ¡t©(_` L
=
+
«¬
( )( y ÕcÁ B(ĵĶ4(#
(1)Ú a 78¥Á B 7 ¡³
(2)Ä L ĦNÜZ[(ÙĦĻÁ A(B 7bCÁ*¦Ø[(#[(aĦĻZ'7ÓÁƎ
x (OQP.[R2 =
3
2QP.22[(ÚĦĻZ[7ĸĆÇ
(1) = (#
(2) = (
+ 3): = (
*)
*;pq<=3401rsŎŏjƏ?34017{|?3401rsÁ7 ¡ÂÃ(
uqEFGHvwxyzD34017{|2I
#1-}Lh(ÄÁ ÅÆ =
+
©(nMN78(MN7ĸĆÇØ
=
+ 3(ĺĻź
= 0(n = 3(MN#7 ¡³
#2-}Lh(~#1-7ĸĆÇØ =
+ 3 =
+ 1) +4(MNZ7ÓÁ ¡Ø
7 (
ĦĻZ7ÓÁƎ
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4 × 7
1
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4
1
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4
7
4 =
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Ù#7ÇØ =
+ 3(
Ä(7 )ÅÆN( = 7 + 3(
N = (
#7ÇØ =
+ 3(
= u( = + 3(
(( + 3)(
= u( = + + 3(
U( + + 3)(
U( = h/ = + + ( + 3) = +7(
(7 )((( + 3)(#(0,3)(
( =
(7) + ( + 3)()
=
2(7)(
0 < < 4(
7 < 0(
( =
2(7)(#( =
() + ( + 3)()
=
2 =
2(
(8#(
U(
=
2(7)8 2
7
= 2³
#3-
ÙĦĻ7ÇØ[ =
+
+ 3 + f(
Á5[ =
+
+ 3 + f(ÁW(
Ù5(g g
+ 3g + 3 + f)(W( S)(
°ıà$5W2ßà(
÷b5$WÔȓ*(O$ = W(
(7 )($(3,3)(
57©ÁØ
g4
2
,
g
3g3f
2
(
$W7©ÁØ
30
2 ,
S3
2
(
g4
2
=
3
2(
g
3g3f
2
=
S3
2 (
Ng = (
Äg = ÅÆ
g
3g3f
2
=
S3
2 (
vĴåNf = S + 3(
S = f*(
~ÏÁĪē7ĬĭÇN$ =
(7) + ()
=
17(
W =
(7) + (S) =
16 + (S + 1)(
$ = W(
$ = W(
16 + (S + 1) = 17(QS + 1 =± 1(
S + 1 = 1u(S = 0(
n0 = f*(
f = 5(
[ =
+
+ 8³
S + 1 = u(
S = (
n = f*(
f = 3(
[ =
+
+ 6³
¢(Ǚ7ÇØ[ =
+
+ 6:[ =
+
+ 8
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