二次函数
的图象
1、已知二次函数
的图象如图所示,对称轴是
,则下列结论中正确的是( ).
A.
B.
C
D.
2、小明从右边的二次函数
图象中,观察得出了下面的五条信息:①
,②
,③函数的最小值为
,④当
时,
,⑤当
时,
(6)对称轴是直线x=2.你认为其中正确的个数为( )
A.2
B.3
C.4
D.5
3、已知二次函数
的图象如图所示,有下列5个结论:①
;②
;③
;④
;⑤
,(
的实数)其中正确的结论有( )
A. 2个
B. 3个
C. 4个
D. 5个
4、如图是二次函数y=ax2+bx+c图象的一部分,图象过点A(-3,0),
对称轴为x=-1.给出四个结论:①b2>4ac;②2a+b=0;③a-b+c=0;④5a<b.其中正确结论是( ).(A)②④
(B)①④
(C)②③
(D)①③
5、二次函数y =ax2+bx+c 的图象如图8所示,且P=| a-b+c |+| 2a+b |,Q=| a+b+c |+| 2a-b |,则P、Q的大小关系为 . P
题
)
21.如图5,已知抛物线
的对称轴为
,点A,B均在抛物线上,且AB与x轴平行,其中点A的坐标为(0,3),则点B的坐标为
A.(2,3)
B.(3,2) C.(3,3)
D.(4,3)
12.二次函数y=ax2+bx+c的图象如图所示,下列结论错误的是
A.ab<0
B.ac<0
C.当x<2时,函数值随x的增大而增大;当x>2时,函数值随x的增大而减小
D.二次函数y=ax2+bx+c的图象与x轴的交点的横坐标就是方程ax2+bx+c=0的根。
24.已知函数y1=x2与函数y2=-
x+3的图象大致如图,若y1<y2,则自变量x的取值范围是( ).
A.-
<x<2
B.x>2或x<-
C.-2<x<
D. x<-2或x>
26二次函数
的图象如图所示,则一次函数
与反比例函数
在同一坐标系内的图象大致为( )
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SHAPE \* MERGEFORMAT
27.(2010 天津)已知二次函数
(
)的图象如图所示,有下列结论:
①
; ②
; ③
; ④
.
其中,正确结论的个数是 (A)1 (B)2 (C)3 (D)4
SHAPE \* MERGEFORMAT
19、(2007贵州省贵阳)二次函数
的图象如图9所示,根据图象解答下列问题:
(1)写出方程
的两个根.(2分)
(2)写出不等式
的解集.(2分)
(3)写出
随
的增大而减小的自变量
的取值范围.(2分)
(4)若方程
有两个不相等的实数根,求
的取值范围.(4分
9.如图所示是二次函数
图形的一部分,图象过A点(3,0),二次函数图象对称轴为x=1,给出四个结论:①
>
;②bc<0;③2a+b=0;④a+b+c=0,其中正确结论是( ).
A.②④ B.①③ C.②③ D.①④
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