如图,抛物线y=ax 2 +bx+2交x轴于A(﹣1,0),B(4,0)两点,交y轴于点C,与...

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热心网友 时间：2024-10-04 00:31

（1）y=﹣ x 2 + x+2，点D坐标为（3，2）（2）p 1 （0，2）；p 2 （ ，﹣2）；p 3 （ ，﹣2）（3）点P坐标为（ ， ），（﹣ ， ）．

试题分析：（1）∵抛物线y=ax 2 +bx+2经过A（﹣1，0），B（4，0）两点，
∴ ，
解得：
∴y=﹣ x 2 + x+2；
当y=2时，﹣ x 2 + x+2=2，解得：x 1 =3，x 2 =0（舍），
即：点D坐标为（3，2）．
（2）A，E两点都在x轴上，AE有两种可能：
①当AE为一边时，AE∥PD，
∴P 1 （0，2），
②当AE为对角线时，根据平行四边形对顶点到另一条对角线距离相等，
可知P点、D点到直线AE（即x轴）的距离相等，
∴P点的纵坐标为﹣2，
代入抛物线的解析式：﹣ x 2 + x+2=﹣2
解得：x 1 = ，x 2 = ，
∴P点的坐标为（ ，﹣2），（ ，﹣2）
综上所述：p 1 （0，2）；p 2 （ ，﹣2）；p 3 （ ，﹣2）．
(3)存在满足条件的点P，显然点P在直线CD下方，设直线PQ交x轴于F，
点P的坐标为（a，﹣ a 2 + a+2），

①当P点在y轴右侧时（如图1），CQ=a，
PQ=2﹣（﹣ a 2 + a+2）= a 2 ﹣ a，
又∵∠CQ′O+∠FQ′P=90°，∠COQ′=∠Q′FP=90°，
∴∠FQ′P=∠OCQ′，
∴△COQ′～△Q′FP， ， ，
∴Q′F=a﹣3，
∴OQ′=OF﹣Q′F=a﹣（a﹣3）=3，CQ=CQ′= = ，
此时a= ，点P的坐标为（ ， ），
②当P点在y轴左侧时（如图2）此时a＜0，，﹣ a 2 + a+2＜0，CQ=﹣a，
PQ=2﹣（﹣ a 2 + a+2）= a 2 ﹣ a，
又∵∠CQ′O+∠FQ′P=90°，∠CQ′O+∠OCQ′=90°，
∴∠FQ′P=∠OCQ已赞过已踩过你对这个回答的评价是？评论收起 // 高质or满意or特型or推荐答案打点时间 window.iPerformance && window.iPerformance.mark('c_best', +new Date); 推荐律师服务：若未解决您的问题，请您详细描述您的问题，通过百度律临进行免费专业咨询 ._1uevpeq{zoom:1;background-color:#fff;border:0;margin-bottom:10px;padding:30px 0 20px 42px;position:relative}._1uevpeq.ec-1841{padding:20px 0}._1uevpeq.ec-2246{padding:20px 0 10px}.ec-1841 .y7we4hu{font-size:16px;margin-bottom:-5px}.y7we4hu{color:#7a8f9a;height:25px;line-height:25px;overflow:hidden;position:relative}.y7we4hu h2{margin:0;padding:0}.y7we4hu:after{clear:both;content:" ";display:block;height:0;visibility:hidden}a.tycfu7u{color:#666;float:right;font-size:12px;margin-left:8px;text-decoration:none}.hhhv6ex{color:#666;font-size:13px;line-height:normal;line-height:20px;margin-top:10px}.vnsdjzp{margin-top:15px;position:relative}.vnsdjzp h3{font-weight:400;padding:0}.vnsdjzp a{text-decoration:none}.vnsdjzp em{color:#d81419;font-style:normal}.ec-2246 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