中考数学复习：二次函数的应用

中考数学复习：二次函数的应用思路点睛1二次函数综合问题一般说应从以下几方面思考（1）：二次函数的基本知识（二次函数定义、图形、性质等）；（2）：坐标系中的知识，最常见的有：“点在线上，则点的坐标适合线的解析式，因此得到方程”；“两线的交点坐标适合两线的解析式”；“求两线的交点坐标需联立解两线的解析式构成的方程组”，“从坐标系中一点作两轴的垂线段，其长度等于横、纵坐标的绝对值”；（3）：几何知识，如勾股定理、直角三角形、三角形（相似三角形是难点）、四边形以及圆的有关知识；（4）：方程的知识：最常用的如解方程（组）、根的判别式、根与系数的关系等；（5）：不等式（组）等。2做二次函数大题时要把题中所给的已知条件列出来，寻找条件和问题之间的关系，同时要把几何图形的性质和代数的知识方法结合起来分析，之后解题。解题的方法有三种。一：设抛物线上存在点p与问题相符，用（x,y）来代替坐标，然后根据前面列出条件的分析来解方程；二：将所要求的量设为x，找出题目中与它相关的量，然后列出另一个二次函数，并化为顶点式，就得到了x的最大最小值或者y的最大最小值；三：结合几何知识，综合分析条件与问题之间的关系。典型试题1发射一枚炮弹，经过x秒后炮弹的高度为y米，x，y满足y=ax2+bx，其中a，b是常数，且a0若此炮弹在第6秒与第14秒时的高度相等，则炮弹达到最大高度的时刻是（ ）A第8秒 B第10秒 C第12秒 D第15秒2已知抛物线y=ax2+bx+c与x轴的两个公共点之间的距离为1若将抛物线y=ax2+bx+c向上平移一个单位，则它与x轴只有一个公共点；若将抛物线y=ax2+bx+c向下平移一个单位，则它经过原点，则抛物线y=ax2+bx+c为（ ）AB或 CD或3如图，在ABC中，C=90，AC=4，BC=2，点A、C分别在x轴、y轴上，当点A在x轴上运动时，点C随之在y轴上运动在运动过程中，点B到原点的最大距离是（ ）A6 B2 C2 D224如图，矩形ABCD中，AB=3，BC=5，点P是BC边上的一个动点（点P不与点B，C重合），现将PCD沿直线PD折叠，使点C落下点C处；作BPC的平分线交AB于点E设BP=x，BE=y，那么y关于x的函数图象大致应为（ ）5如图，已知P的半径为2，圆心P在抛物线y=x2-1上运动，当P与x轴相切时，圆心P的坐标为_6如图，我们把一个半圆与抛物线的一部分围成的封闭图形称为“果圆”已知点A、B、C、D分别是“果圆”与坐标轴的交点，抛物线的解析式为y=x2-2x-3，AB为半圆的直径，则这个“果圆”被y轴截得的弦CD的长为 7.正方形ABCD的边长为1cm，M、N分别是BCCD上两个动点，且始终保持AMMN，当BM= cm时，四边形ABCN的面积最大，最大面积为 cm28如图，在平面直角坐标系xOy中，已知抛物线y=-x2+3x（0x3）在x轴上方的部分，记作C1，它与x轴交于点O，A1，将C1绕点A1旋转180得C2，C2与x 轴交于另一点A2请继续操作并探究：将C2绕点A2旋转180得C3，与x 轴交于另一点A3；将C3绕点A 2旋转180得C4，与x 轴交于另一点A4，这样依次得到x轴上的点A1，A2，A3，An，及抛物线C1，C2，Cn，则点A4的坐标为 ；Cn的顶点坐标为 （n为正整数，用含n的代数式表示） 9如图，排球运动员站在点O处练习发球，将球从O点正上方2 m的A处发出，把球看成点，其运行的高度y（m）与运行的水平距离x（m）满足关系式ya（x6）2h已知球网与O点的水平距离为9 m，高度为243 m，球场的边界距O点的水平距离为18 m来源:学+科+网Z+X+X+K（1）当h26时，求y与x的关系式（不要求写出自变量x的取值范围）来源:学#科#网Z#X#X#K（2）当h26时，球能否越过球网？球会不会出界？请说明理由10如图，在平面直角坐标系中，抛物线与x轴交于A、D两点，与y轴交于点B，四边形OBCD是矩形，点A的坐标为（1，0），点B的坐标为（0，4），已知点E（m，0）是线段DO上的动点，过点E作PEx轴交抛物线于点P，交BC于点G，交BD于点H（1）求该抛物线的解析式；（2）当点P在直线BC上方时，请用含m的代数式表示PG的长度；（3）在（2）的条件下，是否存在这样的点P，使得以P、B、G为顶点的三角形与DEH相似？若存在，求出此时m的值；若不存在，请说明理由真题摘编（2014中考真题）某小商场以每件20元的价格购进一种服装，先试销一周，试销期间每天的销量（件）与每件的销售价x（元/件）如下表：x（元/件）38363432302826t（件）481216202428（1）试求t与x之间的函数关系式；（2）在商品不积压且不考虑其它因素的条件下，每件服装的销售定价为多少时，该小商场销售这种服装每天获得的毛利润最大？每天的最大毛利润是多少？（注：每件服装销售的毛利润=每件服装的销售价-每件服装的进货价）技术官员村位于位于亚运城东部，主干道二以东石楼涌以西的地块，占地面积、m2，总建筑面积、m2，共包括地下室南区、地下室北区、地上部分1栋12栋、服务中心、室外工程等多个单体工程。其中住宅面积m2，共12栋，17栋建筑层数为11层，812栋11层（局部复式顶层），首层局部架空，布置公建配套设施。integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the citys liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the countrys first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for water and the second land of the seven hills. 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, old town-the South Bank Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, suspicious pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the citys liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the countrys first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for water and the second land of the seven hills. 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, old town-the South Bank Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is miss