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12中初三数学第五周周考 白亚云 2015.8.17

12中初三数学第五周周考  白亚云 2015.8.17
12中初三数学第五周周考  白亚云 2015.8.17

初三数学第五周考试试卷

一、选择题,看完四个选项后再做决定呀!(每题3分,共30分)

1.下列函数不属于二次函数的是 ( )

A.y =(x -1)(x +2)

B.y =

2

1(x +1)2 C. y =1-3x 2 D. y =2(x +3)2-2x 2 2. 抛物线()12212++=x y 的顶点坐标是 ( ) A .(2,1) B .(-2,1) C .(2,-1) D .(-2,-1) 3. 函数y =-x 2-4x -3图象顶点坐标是 ( ) A.(2,-1) B.(-2,1) C.(-2,-1) D.(2, 1) 4.已知二次函数)2(2-++=m m x mx y 的图象经过原点,则m 的值为 ( ) A . 0或2 B . 0 C . 2 D .无法确定 5.二次函数c bx x y ++=2的图象上有两点(3,4)和(-5,4),则此拋物线的对称轴是直线 A .1x =- B .1x = C .2x = D .3x = ( ) 6.函数y =2x 2-3x +4经过的象限是 ( ) A.一、二、三象限 B.一、二象限 C.三、四象限 D.一、二、四象限 7.抛物线y =x 2-bx +8的顶点在x 轴上,则b 的值一定为 ( ) A.4 B. -4 C.2或-2 D.42或-42 8.二次函数y =ax 2+bx +c 的图象如图,下列结论错误的是 ( ) A .a >0 B .b >0 C .c <0 D .abc >0 9.已知二次函数y =ax 2+bx +c (a <0)的图象如图,当-5≤x ≤0时,下列说法正确的是 ( ) A .有最小值-5、最大值0 B .有最小值-3、最大值6 C .有最小值0、最大值6 D .有最小值2、最大值6 10.将抛物线y =3x 2向左平移2个单位,再向下平移1个单位,所得抛物线为 ( ) A .y =3(x -2)2-1 B .y =3(x -2)2+1 C .y =3(x +2)2-1 D .y =3(x +2)2+1

(第8题图) (第9题图) (第11题图) (第13题图) (第19题图)

二、填空题,要注意认真审题呀!((每题3分,共18分)

11小兰画了一个函数b ax x y ++=2的图象如图,则关于x 的方程02=++b ax x 的解12、某一型号飞机着陆后滑行的距离y (单位:m )与滑行时间x (单位:s )之间的函数表达式是y =60x 1.5x 2,该型号飞机着陆后需滑行 m 才能停下来.

13、如图,对称轴平行于y 轴的抛物线与x 轴交于(1,0),(3,0)两点,則它的

14、已知点A (a-2b ,2-4ab )在抛物线1042++=x x y 上,则点A 关于

抛物线对称轴的对称点坐标为

15.二次函数y =-x 2+bx +c 的图象如图,则一次函数y =bx +c 的图象不经过第______

象限.

16.如图22-7,在正方形ABCD 中,E 为BC 边上的点,F 为CD 边上的点,且AE =

AF ,AB =4,设EC =x ,△AEF 的面积为y ,则y 与x 之间的函数关系式是_________

三、解答题 ((每题6分,共18分)

17. 已知抛物线2)3(2+-=x a y 经过点(1,-2)

(1)求a 的值;

(2)若点A (m ,y 1)、B (n ,y 2)(m <n <3)都在该抛物线上,试比较y 1与y 2的大小

18.已知二次函数的顶点坐标为(1,4),且其图象经过点(-2,-5),求此二次函数的解析式。

19、拱桥的形状是抛物线,其函数关系式为231x y -=,当水面离桥顶的高度为325m 时,水面的宽度为多少米?

四、简答题,相信自己,我能行!(每题8分,共16分)

20.用长为20cm 的铁丝,折成一个矩形,设它的一边长为xcm ,面积为ycm 2。

(1)求出y 与x 的函数关系式

(2)当边长x 为多少时,矩形的面积最大,最大面积是多少?

21、隧道的截图由抛物线和长方形构成,长方形长是8米,宽2米,抛物线可以4412+-

=x y 表示(1)一辆货车高4米,宽2米,它能通过该隧道吗?

(2)如果该隧道内设双行道,那么这辆货车是否可以通过。

五、简答题,相信自己,我能行!(每题9分,共18分)

22、如图,已知二次函数y=-2

1x 2+bx +c 的图象经过A (2,0)、B (0,-6)两点 (1)求这个二次函数的解析式

(2)设该二次函数的对称轴与x 轴交于点C ,连结BA 、BC ,求△ABC 的面积

(3)抛物线的顶点为点D ,连接BD ,求BD 的长.

23、二次函数的图象与x 轴交于A (-3,0)和B (1,0)两点,交y 轴于点C (0,3),点C 、D 是二次函数图象上的一对对称点,一次函数的图象过点B 、D .

(1)请直接写出D 点的坐标

(2)求二次函数的解析式

(3)根据图象直接写出使一次函数值大于二次函数值的x 的取值范围.

D

六、简答题,相信自己,我做得最好!(每题10分,共20分)

24、已知抛物线C :c bx x y ++-=2经过A (-3,0)和B (0,3)两点,将这条抛物线的顶点记为M ,它的对称轴与x 轴的交点记为N .

(1)求抛物线C 的表达式

(2)求点M 的坐标

(3)将抛物线C 平移到抛物线C ′,抛物线C ′的顶点记为M ′,它的对称轴与x 轴的交点记为N ′.如果以点M 、N 、M ′、N ′为顶点的四边形是面积为16的平行四边形,那么应将抛物线C 怎样平移?为什么?

25. 某校九年级的一场篮球比赛中,如图队员甲正在投篮,已知球出手时离地面高209

m ,与篮圈中心的水平距离为7m ,当球出手后水平距离为4m 时到达最大高度4m ,设篮球运动的轨迹为抛物线,篮圈距地面3m .

(1)建立如图所示的平面坐标系,求抛物线的解析式并判断此球能否准确投中?

(2)此时,若对方队员乙在甲前面1米处跳起盖帽拦截,已知乙的最大摸高为3.1m ,那么他能否获得成功?

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河北省衡水中学2018届高三下学期第7周周考英语答案

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