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1、二 次 函 数单 元 测 试 一一、选择题:1下列函数中,是二次函数的是( ) a. b. c. d. 2. 二次函数,当时,随着的增大而增大,当时,随着的增大而减小,则的值应取( )a12 b11 c10 d9oyxoyxoyxoyx3. 若一次函数的图象经过二、三、四象限,则函数的图象只可能是( ) a. b. c. d.4.在函数y=中,自变量的取值范围是( ) a. -2且3 b. -2且3 c. -2且-3 d. -2且35.无论为何实数,二次函数的图象总是过定点( ) a.(-1,3) b.(1,0) c.(1,3) d.(-1,0)6.在直角坐标系中,坐标轴上到点p(-3,-4)
2、的距离等于5的点共有( ) a.1个 b.2个 c.3个 d.4个7. 下列四个函数中,的值随着值的增大而减小的是( )a b c d cayxo8抛物线的图象如图,oa=oc,则 ( )a b c d以上都不是yoxoyxoyxoyx9.在同一坐标系中,一次函数和二次函数的图象大致为( ) a b c d10若,则二次函数的图象的顶点在 ( )a第一象限 b第二象限 c第三象限 d第四象限二、填空题:11已知二次函数解析式为,则这条抛物线的对称轴为直线= ,满足0的的取值范围是 1x5 ,将抛物线向 上 平移 4 个单位,则得到抛物线。12请写出一个开口向上,对称轴为直线,且与轴的交点坐标为
3、(0,3)的抛物线的解析式 y=(x2)23等 。13. 中,抛物线与轴有两个交点a(2,0)b(-1,0),则的解是_,的解是_。14已知抛物线经过点a(-2,7),b(6,7),c(3,-8),则该抛物线上纵坐标为-8的另一点的坐标是_(1,-8) _。15如右图所示,长方体的底面是边长为cm的正方形,高为6cm,请你用含的代数式表示这个长方体的侧面展开图的面积s=_,长方体的体积为v=_,各边长的和l=_,在上面的三个函数中,_是关于的二次函数。16.抛物线与直线有_个交点,交点坐标是_。三、解答题:17.当二次函数图象与轴交点的横坐标分别是,且与轴交点为(0,-2),求这个二次函数的解
4、析式。18.求抛物线与坐标轴的交点坐标,并求这些交点所构成的三角形面积。19. 一男生推铅球,铅球出手后运动的高度,与水平距离之间的函数关系是,那么这个男生的铅球能推出几米?20.某商场以每件30元的价格购进一种商品,试销中发现,这种商品每天的销售量 (件)与每件的销售价(元)满足一次函数关系,请写出商场卖这种商品每天的销售利润(元)与每件销售价 (元)之间的函数关系式。21如图有一座抛物线形拱桥,桥下面在正常水位是ab宽20米,水位上升3m就达到警戒线cd,这是水面宽度为10米,(1)在如图的坐标系中求抛物线的解析式;(2)若洪水到来时,水位以每小时0.2米的速度上升,从警戒线开始,再持续多
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