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2009п13 κ


2009 п 13-κ κ

12009 壩 x y y=ax2+bx 7 14 (A) 8 (B) 10 (C) 12 (D) 15 22009 Уκ y = 2x 2 λ
2

Ay = 2 x 2 ? 2 By = 2 x 2 + 2 Cy = 2( x ? 2) 2 Dy = 2( x + 2) 2

3 (2009 ) y = ( x ? 2) 2 + 3 2009 ) A23 B23 C23

D23

2 52009 СУκ y = ( x + 1) + 2 С

A2

B1

C3

D

2 3


6(2009 ) y = 2( x + m) 2 + n mn A (mn) B ( ?mn) C (m n) ? D ( ?m n) ?

7(2009 )±еκ y = ax 2 + bx + c x y жκ x 0
? 7 4



x 1 y 1
A B y C y D

1 2

2
? 7 4



82009 κ y = ?3 x 2 ? 6 x + 5



8) A (?1

B (1 8)

C ( ?1 2)

D (1 4) ?

92009 У y=ax1 y=ax2bx1a0

y
1

y
1

y
1

y
1

x

o
A

o
B

x

o
C

x

o
D

x

麯 a > 0 D y=ax1 y=ax2bx1a001 C C 102009
2

By= ?

Ay=x -x-2 Cy= ?

1 2 1 x + +1 2 2
2

1 2 1 x ? x +1 2 2

Dy= ? x + x + 2

112009 Уκ y = ax + bx + c( a 0) У
2

ac > 0 ax + bx + c = 0 0 y x
2

a ? b + c < 0
A4 y B3 C2 D1

O

1

x

12 2009 Уκ y = ax 2 + bx + c 2 A1y1B2 У y2 y1 y2 С A y1 < y 2 B y1 = y 2 C y1 > y 2

D

y 12 2009 κ y = ( x + 1) + 2 С
2

3 O 1 x

A2

B1

C3

D

2 3

4

132009 Уκ yax2bxc(a0) a0. ú x = 1 . x = ?1x = 3 y 0. O

A3 B2 C1 D0

142009 У κ y = ax 2 + bx + c κ y = bx + b 2 ? 4ac y = y

a+b+c x
y x x y x

y x y x

?1

O 1

O A

O B

O C

O D

152009 61 l 2m 4m 62 A y = ?2 x 2 B y = 2 x 2 C y = ?

1 2 x 2

D y =

1 2 x 2

61

62

162009 y = 2 x 2 1 λ A y = 2( x + 1) 2 B y = 2( x ? 1) 2 C y = 2 x 2 + 1 D y = 2 x 2 ? 1

172009 κ y = ax 2 + bx + c a 0 4 b < 0c > 0b ? 4ac > 0 a ? b + c < 0 У
2



A1

B2

C3

D4

18(2009 )=κ yax +bx+c 5 aca+b+c (2009 ) 4a2b+c2a+b2ab У 0 A2 B3 C4 D5

2

19 2009 Т У y = x 2 + x a (a > 0) λ

y = x 2 ? 3 x + 2 a
A1 B2 C3 D4

202009 y = ?2 x 2 + 8 x ? 1 A-27 B-2-25 C27 D2-9 21 2009 y = ax 2 + bx + c

y = bx + b 2 ? 4ac y =
y y
?1

a+b+c x
y y x x



y x

O 1

x

O
A

x

O
B

O
C

O
D

222009 У a 0 У y = ax y = ax 2 п
y
y
?1 ?1

y

y
1

O

x

?1

O

1

x

O

1

x

?1

O

1

x

A

B

C

D

232009 Уй A h = m B k = n C k > n D h > 0k > 0

242009 УУ y = x 2 + x ? 2 x α任 任 y 任 B y = ? x 2 + x ? 2 C y = ? x2 + x + 2 Dy = x 2 + x + 2 A y = ? x 2 ? x + 2

25 2009 Уκ y = ax 2 + bx + c a 0 У b < 0c > 0b ? 4ac > 0 a ? b + c < 0 У
2



A1

B2

C3

D4

262009 κ y = ( x ? 1) 2 ? 2
A(-1-2) B(1-2) C(-12) D(12)

272009 κ y = ( x ? 1) 2 ? 2 A(-1-2) B(1-2) C(-12) D(12)

282009 Уκ y = ( x ? 1) + 2 С
2



A.2

B1

C-1

D-2

292009 УСκ y = ax + bx + c Уó
2

2 c > 1 3 > 0 b 4 a + b + c > 0 5a ? b + c > 0 . 1a < 0 A2 B3 C4 D5

y 1 1 O 1
12

1

2x

30 2009 y2x2 3 λ Ay2x 3
2


2

By2x 3

2

Cy2x3

2

Dy2x3

31(2009 )κ y = ax 2 + bx + c ( a 0) x = 1 D B 2a + b = 0 A c > 0 C b ? 4ac > 0
2

D a ? b + c > 0

y

1

?1

O

1

x

8 32(2009 ) y = a ( x + 1)( x ? 3)( a 0) A x = 1 B x = ?1 C x = ?3 D x = 3

33(2009 )еС 1 СΣСε 81 е A6 B7 C8 D9

34 2009 У y = mx + m y = ? mx + 2 x + 2 m
2

m 0

352009 y = ? x 2 1 λ 3 λ A y = ?( x ? 1) 2 ? 3 C y = ?( x ? 1) 2 + 3 B y = ?( x + 1) 2 ? 3 D y = ?( x + 1) 2 + 3

36 2009 κ y = ax2 + bx + c 6 й A a 0 B. abc 0 C. a + b + c 0 D. b2 ? 4ac 0

372009 κ y = ? 1 x 2 ? x + 3 y = a(x ? h )2 + k 4 A. y = ? 1 ( x ? 2)2 + 2 4 C. y = ? 1 ( x + 2)2 + 4 4 B. y = 1 ( x ? 2)2 + 4 4 D. y = ? 1 x ? 1 ? + 3 ? ? 2? ?2
2

392009 Уκ y = ( x ? 1) 2 + 2 С A.2 B1 C-1 D-2

κ 412009 壩 x y y=ax2+bx 7 14 (A) 8 (B) 10 (C) 12 (D) 15 κ B

432009 y = 3( x ? 1) + 2
2



A x = 1 C x = 2

B x = ?1 D x = ?2

442009 Уκ y = ? x 2 + 2 x ? 2 轫 y = ? x 2 A 2 λ 2 λ B 2 λ 2 λ C 1 λ 1 λ D 1 λ 1 λ 452009 Уκ y = ax 2 + bx + c

a + b + c < 0 a ? b + c > 1 abc > 0 4a ? 2b + c < 0 c ? a > 1
A B C D y 1 1
?1 O

x

462009 κ y = ax 2 + bx + c ( a 0) ж A a < 0 B b < 0 C c < 0 D b ? 4ac < 0
2

47 2009 κ y = ax 2 + bx + c йд Aa0 Bc0 C b2 ? 4ac 0 D a + b + c 0 κ y = ax + bx + c a0 abc
2



y

1

O

1

x

11

D

12009 У x ? 2 x ? 3 ( x ? m ) + k m, k
2

2

m+k =

.

1 1 22009 κ ? ? x 2 4


1 1 3κ ? ? x 2 4
1κ 42009 У y = - 3( x - 1) 2 + 5 __________ 5(2009 )12 y = x 2 ? 2 λ

6 2009 κ y = ax 2 + bx + c x ( ?2 x1 0) ( 0) 1 < x1 < 2 y (0 ·н 4a ? 2b + c = 0 2)

a < b < 0 2a + c > 0 2a ? b + 1 > 0



72009 差У y = ? x 2 + bx + c 6

y x=1

O

3

x

6

82009 У y = (x ? 2)(3 ? x) x = ______ 92009 У д (3 1)
x > 0 y x С 2 С 2 102009 κ y = x ? 2 x ? 3 O0, 0
2



_________________

112009 У x = _____________κ y = x + 2 x ? 2 С У
2

122009 7O 2C1 y= .?

1 2 1 x C2 y=- x2 2 2

132009 12 κ y = ax 2 + bx + c

ab < 0 ax + bx + c = 0 x1 = ?1x2 = 3 a + b + c > 0 x > 1
2

y x y > 0 ?1 < x < 3 У д

14(2009 ) yax 2 +bx+c 3 λ 2 (2009 ) λ yx 2 3x+5 a+b+c=__________

15 2009 У y = ? x 2 + bx + c 8 д У 2 x y

16(2009 ) y = ? x + bx + c 8 д
2

2 x y





17 2009 20cm Σ ΣС cm2 182009 κ y = ax 2 + bx + c x ( ?2 ( x1 0) 0)

2) 1 < x1 < 2 y (0 ·н 4a ? 2b + c = 0
a < b < 0 2a + c > 0 2a ? b + 1 > 0
19 2009 У x ( 6 ? x ) x = е y 20(2009 ) y = ax 2 + bx + c a 0 x

A(?1 B (2 y < 0 x Χ 0) 0)




21(2009 ) y = ax 2 + bx + c a 0 x = 1

( ?1y1 )2y2 ) y1 y2 С y1 (
222009 κ y =

_ y2 ><=

2 2 x 12 A0 3

λ A1 A2 A3 A2008 y B1 B2

2 2 x λ 3 A0 B1 A1 , A1 B2 A2 A2 B3 A3 A2007 B2008 A2008 B3 B2008 κ y =
Σ A2007 B2008 A2008 .

232009 У x ? 2 x ? 3 ( x ? m ) + k m, k
2

2

m+k =

.

24(2009 ) A B y = x 2 ? 4 x + 3 λò A B _____________д

1 1 252009 κ ? ? x 2 4


262009 У y = ax 2 + bx + 3 y = ? x 2 + 3 x + 2 ab С 12009 У 1 Rt ?ABC У A = 90 tan B = κ y = x 2 + 2 x ? 2 272009 x =

3 P AB 4

Q R BC AC APQR Σ AP x APQR y y x 1236 2 1 AB 2 AP APQR оС 2 е1236 1 б ( x, y ) 1 AP APQR 1236 AP = 12 AP APQR . 36 AB . .

C
1

y
2

(12,36)

R A P

Q B
O

x

2 2009 У ?ABC ΣACB = 90 AC = BC , A C x B 3 m m > 0 AB y D P 10 B D 1 A m 2 3 Q P B PQ BC E

BQ AC F FC ( AC + EC )
y
B

E Q D O

A

P

F

C

x

32009 н 20 7 2 6 30 11 1 y x 2 z x

1 z = ? ( x ? 8) 2 + 12 1 x 11 x 8
42009 н y = ? x 2 + bx + c x A(1,0),B(- 30) 1 2裨1е y C QáQAC С Q . 31е PPBC P PBC .У.

26

52009 40 60 300 轵г飺 1 20 1 x y д y x x Χ 2 3 62009 κ ABCD У AB DC AB = 20cmDC = 30cmADC = 45 CD е O AB MN DC 1 O OC x C (15 0) AB 2 3εβΧ 3cm вΧ y M A B N A D O B D 45 20cm 30cm 4 C

C x 4

7 (2009 ) A10B30C0t t 2009 ) 0 tanBAC=3 A C P B 2 l : y = k ( x + 1) m 1 2 Q1n PQ+QB С 3 M l AMP AP h 82009 yx bxc ABCD ABAB x BD P A (02)AB4 (1) (2) SAPO
3 ABCD 2
2

92009 y = ? y =

3 x + 6 x y AB 4

y D Q B C O P E A N x M

5 x AB C A y D 4 E A 1 λ x E x

ABOD PQ PQ PQMN PQMN ACD Sλ

E t 1 C 1 2 0 < t < 5 S t 4 32 S 2
4 t > 0 д ? 4 ? PQMN t Χ3 102009 У 11 M2 - 1 P - 1 2Q PA x QB y AB 1д 2 Q MO MO QáOBQ OAP 3 12 Q е OPOQ OPCQ OPCQ С

? ?

9? 2?

y

y

B

Q
B Q

A

O x

A

O x

M

M

C P

P
11

12

102009 κ A 0 ?2 B ?1 0C 1κ 2ж M1 3 M1

5 9 4 8

1 AC 2

1 l κ EF AB 2

C E BEF Σ

8

11(2009 ) УOBOA OB2OA A ( 12) 1 B 2 AOB 3 AB2е P SABPSABO

12 (2009 ) 2008 Σ г 1 Σ y x x y x OA AB BC AB A BC y = ?5 x + 205 x ? 1230
2

ABC 41012

1ù y x 2д x S xд 3 12 Уù

13(2009 人) 40 50 210 1 10 65 x x y 1 y x д x Χ 2 3 2200 дΧ 2200

14(2009 人) y = ax + bx ? 4a A( ?1 C (0 x 0) 4)
2

B 1 2 D ( mm + 1) D BC 32 BD P DBP = 45 P y

C

A O

B

x

15(2009 ) x A(1 0)E(30) y B(0 3) 1 2 D AEDB 3 AOB DBE ɡ

162009 y = a ( x ? 1)2 + 3 3( a 0) A( ?20) D O OM AD D x OM C B x BC 1 2 P O 1 λ OM P t ( s ) t DAOP ΣΣΣ

3 OC = OB P Q O B 1 λ 2 λ OC BO t ( s ) PQ t BCPQ С С PQ y M D C

P A O Q B x

172009 У A,B,C -1030 03 A,B,C l D l 1 y l 2 AD+CD С D 3 A AD A C AD+CD С BD A У д BD A D ___________ A O B x

182009 κ y = ax 2 + bx + c a 0 A(1 0)

B(2 C (0 2) x = m m > 2 x D 0) ?
1κ 2 x = m m > 2 E E EDB AOC E ú m 3 2 F ABEF Σ m ABEF y

O

x

19 2009 Уκ y = 4 x + 8 x д
2

x

202009 У x A m ? 2 0Bm2 0 C ACBC 1 m 2 m С 0 1е 3 y D máBCD Σ m y D

O A C 25

B

x

202009 УУ OABC 2O A x C y A D OC е 1 2 OABC OB E FG E x x BC FG OE EG 3 H IJ H x x BC IJ K y OK=OHOHIJKC
y C K D E H O F I A x G J B

24

212009 а 100 100 20 10 20 10 20 仯 1 x y1 y2 д y1y2 x 2 x yд y x ɡ

222009 κ y = x 2 + ax + a ? 2 1 a x 2 a<0 x 13 κ 3κ x AB PáPAB

3 13 P ɡ 2

232009 κ y = x 2 ? 2 x ? 1 A κ

y = ax 2 + bx x O C B y = x 2 ? 2 x ? 1
1 A C 2 AOBC y = ax 2 + bx

24 2009 У任 F1 F2 F2 F1 A F2 F1F2 DB C A BD 1 1 F1 y = x 2 任 F2 y = x 2 + bx C (2 0) b ______________ ABCD A B

C

D

2 2 F1 y = ax 2 + c 任 B (2c ? 1) ABD

1 2 2 7 x ? x + 任 AC = 2 3 P AC 3 3 3 P D AD С
3 3 F1 y =

262009 УRtABC б 5б 2 У Уб AB x OA<OB C y 1 OAOB ABC 4 2 D 20 Pmn m>0 n>0 DP BC E BDE д E д 11 CDCPCDP УCDP P Уɡ

1 x + 1 AB AB 2 ABCD AD E C
27 2009 У y = ? У 1д C , D 2 3 5 λ AB D x x · S S t д t Χ 43 C , E y D C A O B x E
1 y = ? x +1 2

28 2009 У 2009 У y = ax 2 ? 5ax + 4a x A C (5 B 4) 1 a P 2д y C5,4 29(2009 ) y = ax 2 + bx + c x A -20-1 0 C DEFG A O P 23 B x

(1)abc

#

. 0 ( > < )
# .

(1)a Χ

302009 12 y = x + 4 x + 3 x AB y C
2

y

x E B ?1 0 1 A 2 xoy P ABC Σ д P 3 CA D M CM DEOC CM 12 312009 A D O C

E

B

x

0) 11 y = ax 2 ? 2ax ? b a > 0 x B ( ?1 y
C D 1д x A 2 AD C E F BAFE Σ F B C D 11 O A x y

32 (2009 ) y = ax 2 + bx ? 3 x A B y C (2 3a ) x = 1 M ? 1 2 C,M x N P PA CN Σ P 3 y = ? x + 3 y D BD E BD A BE BC F ж AEF 4 E y = ? x + 3 3ед

y

A O 1
?3 C

B

x

M

33 2009 У ABC УA = 90 BC = 10 ABC 25 D AB D A B D DE BC AC E DE = x DE ADE ADE DBCE ADE DBCE y 1 x ADE 2 0 < x 5 y x 3 5 < x < 10 y x 3412009 12 + 4 141 y = x 2 ? 2 x + k x AB y C0 ?3 142 143 1 k = A B 2 y = x 2 ? 2 x + k M ABMC 3 x · D ABDC D 4 y = x 2 ? 2 x + k QBCQ BC Σ

141

142

143

352009 10 19 κ y = ?

1 2 x + 2 x 2

x Χ S S Χ

19 362009 18У 5 ABC б C ?1 0 B y = ax 2 + ax ? 2 1 A B 2 3裨2 DDBC 4 ABC A 90 ABC λж B C 2е

18 372009 14ε 120 180 80 е x 1ú x 2 3 6 . 5.7 0.02

14

38(2009 )24У ABC (2009 ) ABC BC 120 AD 80 УɡAHG BHEGFC EFGH ()о EFGH EF BC HG ABAC AHG 6 BHEFCG 10 EFGH 4 (1) FG (2) EFGH FG ABC СС

39(2009 ) OABC AE O BC F (2009 ) CF CFGH BC M CMCFEO CMCO CMNO (1) EOEC С (2) m =

SCFGH

SCNMN

m m

(3)(2) CO1CE

1 2 Q AE QF ymx2+bx+c 3 3

CQ . (4)(3) ymx2+bx+c AB P BC K PBK AEF ? KP y T ?ɡ

402009 У ABCD B40C 2 80D88. y=ax +bx AC . (1)д A (2) P A AB B Q C CD D 1 λ t . P PEAB AC

E
E EFAD F G. t EG ? EQ PQ УжмáCEQ ? д t .

41 OAB 2 Σ A y = ?

3 x + mxE 3

1 E 2 AOE 3 P 2 AE AE OAPE S S 42 2009 y = ? x 2 + 2 x + 3 x A B A B y C D . 1д A B C 2 BC E P BC P PF DE F P m ú m PF m PEDF Σ BCF S S m . 432009 У 2000 2400 8 У 硱. 50 4 1併 x y д y x дΧ 2 4800 3併

442009 У y = ax + bx ? 3 x A B y У
2

C (2 3a ) x = 1 M ? 5 6 C,M x N P PA CN Σ P 7 y = ? x + 3 y D BD E BD A BE BC F ж AEF 8 E y = ? x + 3 3ед
y

A O 1
?3 C

B

x

M

452009 У C y =

6 x

y = ? x 2 ? 2 x + 4 Pn ( x, y ) n = 1 2 C xy ?

1е Pn ( xy ) 2 Pn в 32й
y 6 4 2 x

O

2

4

6

46(2009 )κ y = x + bx + c A ( ?10 ) B ( 3) 0
2

y C 1 b c 2 C CD x D M MCD y

A

0

B x

C

472009 У26 14ε 120 У 180 80 е x 1ú x 2 3 6 . 5.7 0.02

482009 κ y = ax 2 + bx + c е xy ±

x y



?2
4

?1
0

0

1

2 0



?2

?2

κ

49 2009 ABC BC 8BC 6 B C M AB M AB M MN BC AC N AMN У MN x MN h 1ú x h

2 AMN MN AMN BCNM 棬 A A1 A1MN BCNM y x y
A

M

N

B

C

502009 A(-48) B(2n) y = ax 2 (1) a B x P x Q AQ+QB Q (2) y = ax 2 A A B B C(-20) D(-40) x λAC+CB λ ABCD

A

y 8 6 4

2 C D -4 -2 O -2 -4

B 2 4 x

512009 A(-48) B(2n) y = ax 2 (1) a B x P x Q AQ+QB Q (2) y = ax 2 A A B B C(-20) D(-40) x λAC+CB λ ABCD

A

y 8 6 4

2 C D -4 -2 O -2 -4

B 2 4 x

532009 У 13κ y = x 2 + px + q ( p < 0) x AB y C0-1ABC 1κ 2 y M0m y 紹ABC й m Χ 3κ D ABCD Σ D ɡ

5 4

542009 Уκ12 κ

552009 У A 12-1ABC СABC (a)м ABC εСABC (h).ó · S ?ABC = . (1) AB

h B C

1 ah 2

a 12-1

12-2 C(1,4), x A(3,0) y B. (2) P () PAPB P C CAB CD S ?CAB (3) P SPAB= .
y C B D 1 O 1 A x

9 SCAB P 8

12-2

562009 У壬 100 130 80 .г飬 5 20 . 1 2 572009 ABCD Σ AB=2 BC=1 CDG Σ E AB еEMN 仯細 磩MN AB е 1 MN AB 0.5 EMN 2 MN AB x EMN S x

3EMN SУУ
G

M D

N C

A

E 23

B

58 2009 ly=x+mm0 x y AB CM OAAB OC=2CAAM=2MB MCACM M 180 FEM E y , F l ; EO е N, ACM MN PMG P A . F C1 M B C2 P M C3 . (1) 10 m=6 д MF C1 C2 2 m 仯 C1 y x α仯 ɡ C2 C3 е y x С,д x Χ 10

592009 x O y У OABC OA x BCOAOC=ABtanBAO=

4 , B 74 3

1 AC 2 OBC 32е P P еη P

y

C

B

O

G H 24

A

x

60 2009 9 ?ABC 4 E BC EH AC H E EF AC AB F AC P PE = EB

EC = x(0 < x 2)
1 д EF Σ 2

Q AC EFPQ ,EFPQ ú

x
3 2 EFPQ E r E EFPQ r Χ

612009 y· x y = ?50 x + 2600 p· x κ ± · 1 5 3.9 4.3 1 2Σ 12 · 12 · m% 12 · 1.5m% 硱 ò 13% 3 5 · ó 2 · 2 · 1.5 3 5 · 936 m λС ο 34 5.831 35 5.916 37 6.083 38 6.164

622009 xOy У OABC OA y OC x OA=2OC=3 O AOC AB D DC D DEDC OA E 1 EDC 2EDC D y F OC G DF 1е M M

6 5

EF=2GO 32е Gλ Q CQ AB P CG PCG Σ Q
3 2 x bxc AB 4 3 C A 10 C y x3 x Q P 4t

632009 y

BC P PHOB H PB5t 0t1 1 C __b__c__ 2 QH ú t
y
Q
A

H
B

O

x

P
C

3 P 仯 t PHQ COQ t

642009 9-1 y = ax ? 3ax + b A ?1 0C
2

3 ?2 y D x B 1 2 y = kx + 1( k 0) ABCD k

y

A D

O C

B

x

y=kx+1 39-2 E11 EF x FAEF 180 MNQ MNQ AEF MN MG x G MGUAG1U2 MN y
E G A O F Q M N B

x

65. (2009 ) 141 y = x 2 ? 2 x + k x AB y C0 ?3 142 143 1 k = A B 2 y = x 2 ? 2 x + k M ABMC 3 x · D ABDC D 4 y = x 2 ? 2 x + k QBCQ BC Σ



662009 60 涨 45% y x κ y = kx + b x = 65 y = 55 x = 75 y = 45 1κ y = kx + b 2 W д W x 3 500 x Χ 67 2009 κ y = ax + bx + c a 0 A(1 B (2 0) 0)
2

C (0 2) x = m m > 2 x D ?
1κ 2 x = m m > 2 E E EDB AOC E ú m 3 2 F ABEF Σ m ABEF

y

O

x

682009 κ y = ax 2 + bx + c a 0 x AB y C ACBCAC A( ?3 C (03) 0) x = ?4 x = 2 κ y 1 abc 2 M N B 1 λ BABC t MN BMN MN B AC P t P 32κ Q BNQ ABC Q

y C P N

A

M O

B

x

3 P y =

1 2 x P PQ PO x 4

Q P OPQ CDF з P 70(2009 ) y = ?

1 2 2 x + x + 2 x AB y C 2 2

1 ABC 2 ABC Σ 3 C P ABP Σ P y C A O

B

x

712009 η x 2 + px + q + 1 = 0 2 1 q p 2 y = x 2 + px + q x 3 y = x 2 + px + q M x A x1 0B x2 0 AMB С

721 2009 ABCD 4 M N BC CD M BC AM MN 1 Rt ABM RtMCN 2 BM = x ABCN y y x M λ ABCN 3 M λ Rt ABM Rt AMN x

2 2009 β x ? 2 x ? 3 > 0
2

y = x 2 ? 2 x ? 3 y x κ

a = 1 > 0
y = 0 x ? 2 x ? 3 = 0
2

x1 = ?1x2 = 3

y = x 2 ? 2 x ? 3
x < ?1 x > 3 y > 0

x 2 ? 2 x ? 3 > 0 x < ?1 x > 3
1дβ x ? 2 x ? 3 < 0 ____________
2

2β x ? 1 > 0
2

75 2009 1 y = C BC y =

1 2 x + bx + c x AB y 2

1 x ? 2 AC 2 1 BC B __________ C __________
______________ 2ж ABC 3 ABC DEFC DEFG ABC AB ζ [ y = ax + bx + c ? ?
2

b 4ac ? b 2 ? , ?] 4a ? ? 2a ?
y

y

A C

O

B

x

A C

O

B

x

1

2()

76 2009 Χλ 32 Χ Χ ABCD AB x ABCD S 1 S x д x Χ 2 x S

b 4ac ? b 2 οκ y = ax + bx + c a 0 x = ? y(С) = ) 2a 4a
2

77 2009 κ y = x 2 + bx + c A ( ?10 ) B ( 3) 0 y C 1 b c 2 C CD x D M MCD ο ? ?

b 4ac ? b 2 ? ? 4a ? ? 2a
?

782009 17· 6 OM 12 . O x OM . . . (1)д M P (2) (3)ΡAD- DC- CB CD AB OM

77 2009 25.κ D(0 7 3 ) C 4 9 x AB 6. κ P PA+PD С P QQAB ABC Q

x = ?1

82009 x AB y C

A ( ?3) C ( 0 2 ) 0 ?
1 2 P PBC С P 3 D OC O C D DE PC x E PD PE CD m PDE S S m S y

A

O

B

x

C

92009 y = x 2 + bx + c A(1 B (0 0) 2) D 1 2 OAB A 90 B C λ y C 3裨2 y B1 D1 N NBB1 NDD1 2 N y

B

O

A D 26

x

832009 У 13κ y = x + px + q ( p < 0) x AB
2

y C0-1ABC 1κ

5 4

2 y M0m y 紹ABC й m Χ 3κ D ABCD Σ D ɡ 4.2009 Уκ1 2κ

5.2009 У 12-1ABC A СABC (a)м ABC εСABC (h).ó · S ?ABC = . (1) AB

h B C

1 ah 2

a 12-1

12-2 C(1,4), x A(3,0) y B. (2) P () PAPB P C CAB CD S ?CAB (3) P SPAB= .
y C B D 1 O 1 A x

9 SCAB P 8

12-2

892009 У壬 100 130 80 .г飬 5 20 . 1 2

902009 У 1 Rt ?ABC У A = 90 tan B =

3 P AB 4

Q R BC AC APQR Σ AP x APQR y y x 1236 2 1 AB 2 AP APQR оС 2 е1236 1 б ( x, y ) 1 AP APQR 1236 AP = 12 AP APQR . 36 AB . .

C

y
(12,36)

R A
1

Q P B
O
2

x

3.2009 У ?ABC Σ ACB = 90 AC = BC , A C x B 3 m m > 0 AB y D P 10 B D 1 A m 2

3 Q P B PQ BC E

BQ AC F FC ( AC + EC )
y
B

E Q D O

A

P

F

C

x

93. 2009 н 20 7 2 6 30 11 1 y x 2 z x

1 z = ? ( x ? 8) 2 + 12 1 x 11 x 8
94 2009 н y = ? x 2 + bx + c x A(1,0),B(- 3 0) 1 2裨1е y C QáQAC С Q . 31е PPBC P PBC .У. κй

C

B

A

26

95(2009 ) C1 y = a ( x + 2 ) ? 5 P x (2009 )
2

AB A B B 1 1Pa4 21 C2 C1 x C2 C3C3 M PM B C3 4 32 Q x C1 Q 180 C4 C4 N x EF E F PNF Q 5 κ,

C1

y M B O P 11 x

C1

y N A O P 2 2 B Q E F x

A

C2

C3

C4

C1
A

y H O P (1) B

M

G

x

C2

C3

1 C1 y = a (x + 2 ) ? 5 P -2-5 B10 C1 0 = a (1 + 2)2 ? 5 5 a 9 2 PM PHx H MGx G PM B PM B PBMB PBHMBG
2

MGPH5BGBH3 M 45 C1 C2 C1 x C3 C2

y N A H B Q G E O K

5 C3 y = ? ( x ? 4)2 + 5 9

3 C4 C1 x Q 180 NP Q 2 N 5 P N m5 PHx H NGx G (2) PKNG K Q x EFAB2BH6 FG3 F m+30 H 20K m-5 PN2NK2+PK2m2+4m+104 PF2PH2+HF2m2+10m+50 NF252+3234 44 19 PNF90?PN2+ NF2PF2 m Q 0 3 3 10 2 PFN90?PF2+ NF2PN2 m Q 0 3 3 PNNK10NFNPF90? 19 2 Q 0 0 PNF 3 3 Σ 4.(2009 ) ? 4.(2009 ) y = ax 2 + bx A ( ?3 3) P t0 t 0 1 A 12 y С д t 2 t = ? 4 ab 3д t
P -3

F x

C4

y

O

x

-3 A

12

98(2009 ) xOy У 1 O

ABCD y = ax + bx + c y D
2

y = x M N MANC O A C 1 2 x E DE DE O F EF 3 B O DC P ж P y D E A M O B C F x N

9909 OABC O(00)A( C(
7 2

3 2

1) B(st)

0) y=x2mxm P OABC m

(1) s t л OABC (2) y=x2mxm OABC AB m Χ

24

100 09 11

y = ( x + m) 2 + k ? m 2 x A( x1 B( x2 y 0) 0)
C ABC P 1 P y D 2 AB P ABC 5 m k

S ABC =

1 1 AB OC = 2 m 2 + 1 1 = 5 m = 2. 2 2

10109 l y = ? x + 4 x y AB l m O x 1 λ x y M N t 0 < t 4 1 AB 2ú t MON S1 3 MN m OMPN MPN OAB S2 2 < t 4 S2 t m У t S2 OAB N O P M A x l y B l m N O y B E P P F M A x

5 16

1022009 231 1Тκ壮

2д w mkg лú Χ 3飬 2 60kg 2009 P a + 1 a ? 1 x

8 y = ? ( x > 0) x
y x y = k 2 x 2 ? (2k + 1) x + 1 ApB P
PAB .

2009 г 0.1 5

34 40 ò y x 1 x 12

? ?0.05 x + 0.25 (1 x < 4) ? y = ? 0.1 (4 x 6) p x ?0.015 x + 0.01 (6 < x 12) ?
仯 д p x w x ж

p
40 36 20 4 12

x

2009 У y = x 2 y = 1 Χ OABC O x 1 λ O1 A1 B1C1 н 90 A O1 (1 0) C O1 BA1 B1 y B C1 (2 1) ? D OC OCA1 B1 3

A ? 11 B

C 11 A1 O1 B1 x C1

O

1032009 У±

2100/ 2400/ 800/ 1100/ 200/ 100/
豸 20000









1ó x y1 y2 y1

y2 x =-6
2ó 400 700 4 104 2009 У Rt ABC УBAC = 90 C = 60 BC = 24 P BC P BC P PD BA AC D 2 1 ABC DAP APD 2 PC APD 4 3 AC BP У BP 4

A D

60 B P C

10512009 У y = ax 2 + bx + 3 a0 x

A(10) B (30) y C (1) (2) x M PCMP Σдз P (3) E BECE BOCE E

1072009 У y2 г 飮鷢 y1 · x y = ? 25 24

1 y2 = x 2 + bx + c 8

3 x + 36 8

y2 · x

O 1 2 3 4 5 6 7 8 9 10 11 12 x 2

1 bc 2 y · x 3塤·

1082009 У 9 OABC У A C

0) 2) P AOC O A(4C (0 D OA е

1 P δ PC PD y OPD 2 P B С C (0 2) 3 E 2 P δ PDE С P PDE O 4 N OABC P CPN = 90 д P 109192009 У1лκ У

B P D 9
A(4 0)

x

y = ? x 2 + 2 x
2л y = ? x 2 + 2 x λ 3д. С1. y

O

x

19

1102009 ABCD 4 M N BC CD M BC AM MN 1 Rt ABM RtMCN 2 BM = x ABCN y y x M λ ABCN 3 M λ Rt ABM Rt AMN x A D

N B M C

111 2009 гг飬 y x

y = 0.3 x y x

y = ax 2 + bx a 0ab x 1 y 1.4
x 2 y 2.6 1 y x 2г 10 t д W t
2 1122009 У x y = ax + x + 1 a

1 x a 2 x a Χ

1132009 У裬 磬涨磬 y x κ x Z Z x κ y() 1200 800 200 x() 0 400 x() 1δ 0 2 y Z x 3 w x w z() 200 160

1132009 У ABCD У A x D y AB y EBC x F OE = 1

y = ax + bx ? 4 ADF
2

13 2Q DF Q x AD M BC N SAFQM =

3 S FQN ж AFQM 3 2 3 DB P CB H AP PH AP = PH 4
y B F C O D 114(2009 )У O AB
A(0 B (?2 AB 4) 0)

E A x

1 AOB A 90 AO1 B1 AO1 B1 д B1 O1 2 B A O1

O x 115 20 09 A21 B

1 2 MMOB AOB 3 3 OAAB x · NOBN OAB N y O A B x

24


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