专题复习_二次函数图象与性质_一对一_讲义.doc

专业好文档与二次函数系数相关代数式符号的判定（一）二次函数的图象与各项系数之间的关系 1. 二次项系数二次函数中，作为二次项系数，显然 当时，抛物线开口向上，的值越大，开口越小，反之的值越小，开口越大； 当时，抛物线开口向下，的值越小，开口越小，反之的值越大，开口越大总结起来，决定了抛物线开口的大小和方向，的正负决定开口方向，的大小决定开口的大小2. 一次项系数 在二次项系数确定的前提下，决定了抛物线的对称轴 在的前提下，当时，即抛物线的对称轴在轴左侧；当时，即抛物线的对称轴就是轴；当时，即抛物线对称轴在轴的右侧 在的前提下，结论刚好与上述相反，即当时，即抛物线的对称轴在轴右侧；当时，即抛物线的对称轴就是轴；当时，即抛物线对称轴在轴的左侧总结起来，在确定的前提下，决定了抛物线对称轴的位置的符号的判定：对称轴在轴左边则，在轴的右侧则，概括的说就是“左同右异”总结： 3. 常数项 当时，抛物线与轴的交点在轴上方，即抛物线与轴交点的纵坐标为正； 当时，抛物线与轴的交点为坐标原点，即抛物线与轴交点的纵坐标为； 当时，抛物线与轴的交点在轴下方，即抛物线与轴交点的纵坐标为负 总结起来，决定了抛物线与轴交点的位置 总之，只要都确定，那么这条抛物线就是唯一确定的（二）二次函数与一元二次方程1. 二次函数与一元二次方程的关系（二次函数与轴交点情况）：一元二次方程是二次函数当函数值时的特殊情况.图象与轴的交点个数： 当时，图象与轴交于两点，其中的是一元二次方程的两根这两点间的距离. 当时，图象与轴只有一个交点； 当时，图象与轴没有交点. 当时，图象落在轴的上方，无论为任何实数，都有； 当时，图象落在轴的下方，无论为任何实数，都有 二、温故知新 1你能说出函数y4(x2)21图象的开口方向、对称轴和顶点坐标吗？ 2函数y4(x2)21图象与函数y4x2的图象有什么关系? 3函数y4(x2)21具有哪些性质?4不画出图象，你能直接说出函数yx2x的图象的开口方向、对称轴和顶点坐标吗?来源:jg+xf+w.com5你能画出函数yx2x的图象，并说明这个函数具有哪些性质吗?三、讲练结合（一）、a，b，c的符号的判定例1、已知a0，b0，c0，那么抛物线y=ax2+bx+c的顶点在（）a第一象限b第二象限c第三象限d第四象限例2、（潍坊）已知二次函数y=ax2+bx+c的图象如图1所示，则a，b，c满足（）aa0，b0，c0ba0，b0，c0ca0，b0，c0da0，b0，c0练习：1、二次函数y=ax2+bx+c（a）的图象如图2所示，则点在（）a第一象限b第二象限c第三象限d第四象限2、（2008年陕西省）已知二次函数（其中），关于这个二次函数的图象有如下说法：图象的开口一定向上；图象的顶点一定在第四象限；图象与轴的交点至少有一个在轴的右侧以上说法正确的个数为（ ）a0b1c2d3（二）、的符号的判定例1、下图中的是（ ）yxoyxyxoyxoo（a） （b） （c） （d）练习：不论x为何值,函数y=ax2+bx+c(a0)的值恒大于0的条件是( ) a.a0,0; b.a0, 0; c.a0; d.a0, 0, b0时,下列图象有可能是抛物线y=ax2+bx+c的是（）y0 11x-1图1 3、二次函数的图象如图1所示，则下列结论中，正确的个数是（ ）；（a）4（b）3（c）2 （d）1 4、 (2002黄冈改编)已知二次函数的图象如图2所示，那么下列判断不正确的是（ ）(a)abc0； （b）0； (c)2a+b0； （d）0oxy-115、二次函数的图象如图所示，则 ，这四个式子中，值为正数的有（ ）图2 a4个b3个c2个d1个6、二次函数y=ax2+bx+c的图象如图3所示，则下列关于a，b，c间关系的判断正确的是（）aab0bbc0ca+b+c0da-b+c07、(2008年安徽省)如图为二次函数y=ax2bxc的图象，在下列说法中： ac0； 方程ax2bxc=0的根是x1= 1, x2= 3 abc0 当x1时，y随x的增大而增大。正确的说法有_。(把正确的答案的序号都填在横线上) winger tuivasa-sheck, who scored two tries in the kiwis 20-18 semi-final win over england, has been passed fit after a lower-leg injury, while slater has been named at full-back but is still recovering from a knee injury aggravated against usa.both sides boast 100% records heading into the encounter but australia have not conceded a try since josh charnleys effort in their first pool match against england on the opening day.aussie winger jarryd hayne is the competitions top try scorer with nine, closely followed by tuivasa-sheck with eight.but it is recently named rugby league international federation player of the year sonny bill williams who has attracted the most interest in the tournament so far.the kiwi - with a tournament high 17 offloads - has the chance of becoming the first player to win the world cup in both rugby league and rugby union after triumphing with the all blacks in 2011.id give every award back in a heartbeat just to get across the line this weekend, said williams.the (lack of) air up there watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its about how he felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs governing body, has also ordered an immediate investigation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska. baumgartner the disappointing news: mission aborted.the supersonic descent could happen as early as sunda.the weather plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto something resembling an olympic diving platform.they blew it in 2008 when they got caught cold in the final and they will not make the same mistake against the kiwis in manchester.five years ago they cruised through to the final and so far history has repeated itself here - the last try they conceded was scored by englands josh charnley in the opening game of the tournament.that could be classed as a weakness, a team under-cooked - but i have been impressed by the kangaroos focus in their games since then.they have been concentrating on the sort of stuff that wins you tough, even contests - strong defence, especially on their own goal-line, completing sets and a good kick-chase. theyve been great at all the unglamorous stuff that often goes unnoticed in the stands but not by your team-mates.it is as though their entire tournament has been preparation for the final.in johnathan thurston, cooper cronk, cameron smith and either billy slater or greg inglis at full-back they have a spine that is unmatched in rugby league. they have played in so many high-pressure games - a priceless ass