3.5 待定系数法
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1 (-2,8), .
y=kx,k . y=kx (-2,8) 8=k�(-2) k=-4 y=-4x
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2 y=f(x),f(1)=3,f(3)=5, .
y=kx+b f(1)=3,f(3)=5
() = + = () = + =
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18.(6,-12),x (8,0),.
(6,-12) y=a(x-6)2-12 x(8,0) 0=a(8-6)2-12 a=3 y=3(x-6)2-12 y=3x2-36x+96.
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19.f(x-2)=x2-7x+13,f(x).
B
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2.f(x)=3x2-x-2=(x-1)(ax+b),a,b ( ) A.a=3,b=2 B.a=3,b=-2 C.a=2,b=3 D.a=2,b=-3
A
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3.f(x)=ax+b,f(0)=-2,f(3)=4,f(1)= ( ) A.4 B.-4 C.2 D.0
9.y=ax2+bx+c(a>0),t f(2+t)=f(2-t), ( )
A.f(2)<f(-1)<f(4) B.f(-1)<f(2)<f(4) C.f(2)<f(4)<f(-1) D.f(4)<f(2)<f(-1)
C
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10.y=ax2-4x+1,a ()
A.(-,0) B.(0,+) C.(-,+) D.[0,+)
x-2=t,x=t+2 f(x-2)=x2-7x+13 f(t)=(t+2)2-7(t+2)+13=t2-3t+3 f(x)=x2-3x+3
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3.4
1.. 2..
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1.,,, ,,. .
. 2.: (1):y=kx(k0) (2):y=(k0)
(3):y=kx+b(k0)
(4):
:y=ax2+bx+c(a0) :y=a(x-m)2+n(a0),(m,n). :y=a(x-x1)(x-x2), x1x2 ax2+bx+c=0 , x .
:a=-,b=3,c=
y=-x2+3x+.
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17.y=ax2+bx+c,, (1)yx; (2)yx; (3)yx; (4)y=ax2+bx+c .
(1),a=0,c=0b0,; (2),a=0,b0,; (3)a0,; (4)a>0b=0,c=0,y=ax2+bx+c .
B
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11. y=ax2+bx+c (1,-1)(2,1)(3,7),
a= 2
,b= -4
,c= 1
.
12. y=ax2+bx+c (2,3),
x , 1,
a= -3 ,b= 12 ,c= -9
.
13. y=ax2+bx+c (0,24), x=,y
25, a= -4
y=-2(x+2)(x-3)
a=-2
: . .
(1),, ,3;
(2) ,.4;
(3)xax2+bx+c=0 ,.5.
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6 f(x+1)=x2-2x-5,f(x).
f(x+1)=x2-2x-5=x2+2x+1-4x-4-2=(x+1)2-4(x+1)-2 f(x)=x2-4x-2
D
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4.y=ax+by=bx+a ( )
B
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5.,y=ax+ y=ax2 ( )
A.
B.
C.
D.
A
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6.y=-ax(2,-16),a= ( ) A.2 B.-2 C.4 D.-4
C
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,b= 4
,
c= 24
.
14.(m,-5)(2,3),
m=
-
.
15. A(1,0),B(3,0),C(0,3),
y=x2-4x+3 .
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16.A(1,6),B(2,5),C(-1,0) ,.
y=ax2+bx+c
+ + =
: + + =
wenku.baidu.com + =
= =
y=x+2
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3 y=f(x),(-2,20) (1,2)(3,0),.
y=ax2+bx+c(a0),(-2,20)
(1,2)(3,0)
- + =
=
+ + =
= -
+ + =
y=x2-5x+6
=
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4 (-1,-2),(2,5), .
(-1,-2) y=a(x+1)2-2(a0)
(2,5)
5=a(2+1)2-2 a=
y=(x+1)2-2
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5 x(-2,0)(3,0), (-1,8),.
x(-2,0)(3,0) y=a(x+2)(x-3)
(-1,8) 8=a(-1+2)(-1-3)
7."ac<0""y=ax2+bx+c(a0)x
" ( )
A. B.
C.
D.
A
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8.f(x+1)=x2-5x+4,f(x) ( ) A.f(x)=x2-7x+10 B.f(x)=x2-7x-10 C.f(x)=x2+7x-10 D.f(x)=x2-4x+6
A
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t=x+1,x=t-1, f(x+1)=x2-2x-5 xf(t)=(t-1)2-2(t-1)-5=t2-4t-2 f(x)=x2-4x-2
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1.(2,3),(3,1),
()
A.y=2(x-2)2+3
B.y=-2(x-2)2+3
C.y=2(x+2)2+3 D.y=-2(x+2)2+3
1 (-2,8), .
y=kx,k . y=kx (-2,8) 8=k�(-2) k=-4 y=-4x
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2 y=f(x),f(1)=3,f(3)=5, .
y=kx+b f(1)=3,f(3)=5
() = + = () = + =
� www.gzshuyou.com
18.(6,-12),x (8,0),.
(6,-12) y=a(x-6)2-12 x(8,0) 0=a(8-6)2-12 a=3 y=3(x-6)2-12 y=3x2-36x+96.
� www.gzshuyou.com
19.f(x-2)=x2-7x+13,f(x).
B
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2.f(x)=3x2-x-2=(x-1)(ax+b),a,b ( ) A.a=3,b=2 B.a=3,b=-2 C.a=2,b=3 D.a=2,b=-3
A
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3.f(x)=ax+b,f(0)=-2,f(3)=4,f(1)= ( ) A.4 B.-4 C.2 D.0
9.y=ax2+bx+c(a>0),t f(2+t)=f(2-t), ( )
A.f(2)<f(-1)<f(4) B.f(-1)<f(2)<f(4) C.f(2)<f(4)<f(-1) D.f(4)<f(2)<f(-1)
C
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10.y=ax2-4x+1,a ()
A.(-,0) B.(0,+) C.(-,+) D.[0,+)
x-2=t,x=t+2 f(x-2)=x2-7x+13 f(t)=(t+2)2-7(t+2)+13=t2-3t+3 f(x)=x2-3x+3
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3.4
1.. 2..
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1.,,, ,,. .
. 2.: (1):y=kx(k0) (2):y=(k0)
(3):y=kx+b(k0)
(4):
:y=ax2+bx+c(a0) :y=a(x-m)2+n(a0),(m,n). :y=a(x-x1)(x-x2), x1x2 ax2+bx+c=0 , x .
:a=-,b=3,c=
y=-x2+3x+.
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17.y=ax2+bx+c,, (1)yx; (2)yx; (3)yx; (4)y=ax2+bx+c .
(1),a=0,c=0b0,; (2),a=0,b0,; (3)a0,; (4)a>0b=0,c=0,y=ax2+bx+c .
B
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11. y=ax2+bx+c (1,-1)(2,1)(3,7),
a= 2
,b= -4
,c= 1
.
12. y=ax2+bx+c (2,3),
x , 1,
a= -3 ,b= 12 ,c= -9
.
13. y=ax2+bx+c (0,24), x=,y
25, a= -4
y=-2(x+2)(x-3)
a=-2
: . .
(1),, ,3;
(2) ,.4;
(3)xax2+bx+c=0 ,.5.
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6 f(x+1)=x2-2x-5,f(x).
f(x+1)=x2-2x-5=x2+2x+1-4x-4-2=(x+1)2-4(x+1)-2 f(x)=x2-4x-2
D
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4.y=ax+by=bx+a ( )
B
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5.,y=ax+ y=ax2 ( )
A.
B.
C.
D.
A
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6.y=-ax(2,-16),a= ( ) A.2 B.-2 C.4 D.-4
C
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,b= 4
,
c= 24
.
14.(m,-5)(2,3),
m=
-
.
15. A(1,0),B(3,0),C(0,3),
y=x2-4x+3 .
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16.A(1,6),B(2,5),C(-1,0) ,.
y=ax2+bx+c
+ + =
: + + =
wenku.baidu.com + =
= =
y=x+2
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3 y=f(x),(-2,20) (1,2)(3,0),.
y=ax2+bx+c(a0),(-2,20)
(1,2)(3,0)
- + =
=
+ + =
= -
+ + =
y=x2-5x+6
=
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4 (-1,-2),(2,5), .
(-1,-2) y=a(x+1)2-2(a0)
(2,5)
5=a(2+1)2-2 a=
y=(x+1)2-2
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5 x(-2,0)(3,0), (-1,8),.
x(-2,0)(3,0) y=a(x+2)(x-3)
(-1,8) 8=a(-1+2)(-1-3)
7."ac<0""y=ax2+bx+c(a0)x
" ( )
A. B.
C.
D.
A
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8.f(x+1)=x2-5x+4,f(x) ( ) A.f(x)=x2-7x+10 B.f(x)=x2-7x-10 C.f(x)=x2+7x-10 D.f(x)=x2-4x+6
A
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t=x+1,x=t-1, f(x+1)=x2-2x-5 xf(t)=(t-1)2-2(t-1)-5=t2-4t-2 f(x)=x2-4x-2
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1.(2,3),(3,1),
()
A.y=2(x-2)2+3
B.y=-2(x-2)2+3
C.y=2(x+2)2+3 D.y=-2(x+2)2+3