{"ID":"d7f7f5ba-3d16-417d-b583-060c66aab80f","Content":"<img alt=\"菁优网\" src=\"http://img.jyeoo.net/quiz/images/201706/117/45c812d2.png\" style=\"vertical-align:middle;FLOAT:right\" />已知抛物线y=<span class=\"MathJye\" mathtag=\"math\" style=\"whiteSpace:nowrap;wordSpacing:normal;wordWrap:normal\"><table cellpadding=\"-1\" cellspacing=\"-1\" style=\"margin-right:1px\"><tr><td style=\"border-bottom:1px solid black\">1</td></tr><tr><td>4</td></tr></table></span>x<SUP>2</SUP>+1具有如下性质：该抛物线上任意一点到定点F（0，2）的距离与到x轴的距离始终相等，如图，点M的坐标为（<span dealflag=\"1\" class=\"MathJye\" mathtag=\"math\" style=\"whiteSpace:nowrap;wordSpacing:normal;wordWrap:normal\"><table cellspacing=\"-1\" cellpadding=\"-1\"><tr><td style=\"font-size: 0px\"><div hassize=\"7\"><div style=\"width:6px;background: url('http://img.jyeoo.net/images/formula/part/8730U.png') repeat-y; height: 1px;overflow: hidden\" muststretch=\"v\"></div><div style=\"width:6px;background: url('http://img.jyeoo.net/images/formula/part/8730D.png') no-repeat; height: 7px; overflow: hidden\"></div></div></td><td style=\"padding:0;padding-left: 2px; border-top: black 1px solid;line-height:normal\">3</td></tr></table></span>，3），P是抛物线y=<span class=\"MathJye\" mathtag=\"math\" style=\"whiteSpace:nowrap;wordSpacing:normal;wordWrap:normal\"><table cellpadding=\"-1\" cellspacing=\"-1\" style=\"margin-right:1px\"><tr><td style=\"border-bottom:1px solid black\">1</td></tr><tr><td>4</td></tr></table></span>x<SUP>2</SUP>+1上一个动点，则△PMF周长的最小值是（　　）","Method":"解：过点M作ME⊥x轴于点E，交抛物线y=<span class=\"MathJye\" mathtag=\"math\" style=\"whiteSpace:nowrap;wordSpacing:normal;wordWrap:normal\"><table cellpadding=\"-1\" cellspacing=\"-1\" style=\"margin-right:1px\"><tr><td style=\"border-bottom:1px solid black\">1</td></tr><tr><td>4</td></tr></table></span>x<SUP>2</SUP>+1于点P，此时△PMF周长最小值，<img alt=\"菁优网\" src=\"http://img.jyeoo.net/quiz/images/201706/139/44244d24.png\" style=\"vertical-align:middle;FLOAT:right\" /><br />∵F（0，2）、M（<span dealflag=\"1\" class=\"MathJye\" mathtag=\"math\" style=\"whiteSpace:nowrap;wordSpacing:normal;wordWrap:normal\"><table cellspacing=\"-1\" cellpadding=\"-1\"><tr><td style=\"font-size: 0px\"><div hassize=\"7\"><div style=\"width:6px;background: url('http://img.jyeoo.net/images/formula/part/8730U.png') repeat-y; height: 1px;overflow: hidden\" muststretch=\"v\"></div><div style=\"width:6px;background: url('http://img.jyeoo.net/images/formula/part/8730D.png') no-repeat; height: 7px; overflow: hidden\"></div></div></td><td style=\"padding:0;padding-left: 2px; border-top: black 1px solid;line-height:normal\">3</td></tr></table></span>，3），<br />∴ME=3，FM=<span dealflag=\"1\" class=\"MathJye\" mathtag=\"math\" style=\"whiteSpace:nowrap;wordSpacing:normal;wordWrap:normal\"><table cellspacing=\"-1\" cellpadding=\"-1\"><tr><td style=\"font-size: 0px\"><div hassize=\"7\"><div style=\"width:6px;background: url('http://img.jyeoo.net/images/formula/part/8730U.png') repeat-y; height: 1px;overflow: hidden\" muststretch=\"v\"></div><div style=\"width:6px;background: url('http://img.jyeoo.net/images/formula/part/8730D.png') no-repeat; height: 7px; overflow: hidden\"></div></div></td><td style=\"padding:0;padding-left: 2px; border-top: black 1px solid;line-height:normal;padding-top:1px\">(<table cellspacing=\"-1\" cellpadding=\"-1\"><tr><td style=\"font-size: 0px\"><div hassize=\"7\"><div style=\"width:6px;background: url('http://img.jyeoo.net/images/formula/part/8730U.png') repeat-y; height: 1px;overflow: hidden\" muststretch=\"v\"></div><div style=\"width:6px;background: url('http://img.jyeoo.net/images/formula/part/8730D.png') no-repeat; height: 7px; overflow: hidden\"></div></div></td><td style=\"padding:0;padding-left: 2px; border-top: black 1px solid;line-height:normal\">3</td></tr></table>-0<span><span>)</span><span style=\"vertical-align:super;font-size:90%\">2</span></span>+(3-2<span><span>)</span><span style=\"vertical-align:super;font-size:90%\">2</span></span></td></tr></table></span>=2，<br />∴△PMF周长的最小值=ME+FM=3+2=5．<br />故选C．","Analyse":"过点M作ME⊥x轴于点E，交抛物线y=<span class=\"MathJye\" mathtag=\"math\" style=\"whiteSpace:nowrap;wordSpacing:normal;wordWrap:normal\"><table cellpadding=\"-1\" cellspacing=\"-1\" style=\"margin-right:1px\"><tr><td style=\"border-bottom:1px solid black\">1</td></tr><tr><td>4</td></tr></table></span>x<SUP>2</SUP>+1于点P，由PF=PE结合三角形三边关系，即可得出此时△PMF周长取最小值，再由点F、M的坐标即可得出MF、ME的长度，进而得出△PMF周长的最小值．","Discuss":"本题考查了二次函数的性质以及三角形三边关系，根据三角形的三边关系确定点P的位置是解题的关键．","Degree":0.60,"Cate":1,"Label":"（2017•泸州）","LabelYear":2017,"VIP":0,"Remark":"","Answer":"<sl><Answer><c><string>2</string></c><o><string>3</string><string>4</string><string>5</string><string>6</string></o></Answer></sl>","Origin":1,"Source":1,"Source2":0,"RC":2.00,"EC":0.00,"GC":0.00,"YZ":false,"CPID":null,"U0ID":"0a468a86-c751-4810-85e4-dbd6a67bbb04","U0RQ":"2017-06-15T10:33:08.157","U1ID":"e79e1952-66f5-40ae-9d3a-2e26b28028bb","U1RQ":"2017-06-15T13:30:02.9","U2ID":"24fa4335-a21a-4ab0-8556-445fec977225","U2RQ":"2017-06-17T11:20:11.65","U3ID":"9c78c48c-dcc6-4350-a332-d7d8128a67d3","U3RQ":"2017-06-17T11:29:38.913","U4ID":null,"U4RQ":null,"U5ID":null,"U5RQ":null,"U6ID":null,"U6RQ":null,"U7ID":"9c78c48c-dcc6-4350-a332-d7d8128a67d3","U7RQ":"2017-06-17T11:29:38.913","Error":0,"Flags":"170   ","ATMP":0,"Date":"2017-06-14T13:02:10.343","Status":88,"Demand":"","UseTime":0,"Batch":20,"UTSA":"2017-09-06T05:03:00.82","SyncDate":null,"QuesPoints":[{"QuesID":"d7f7f5ba-3d16-417d-b583-060c66aab80f","PointNo":"H3","Major":true,"Point":{"No":"H3","Name":"二次函数的性质","Desc":"二次函数y=ax<SUP>2</SUP>+bx+c（a≠0）的顶点坐标是（-$\\frac{b}{2a}$，$\\frac{4ac-{b}^{2}}{4a}$），对称轴直线x=-$\\frac{b}{2a}$，二次函数y=ax<SUP>2</SUP>+bx+c（a≠0）的图象具有如下性质：<br />①当a＞0时，抛物线y=ax<SUP>2</SUP>+bx+c（a≠0）的开口向上，x＜-$\\frac{b}{2a}$时，y随x的增大而减小；x＞-$\\frac{b}{2a}$时，y随x的增大而增大；x=-$\\frac{b}{2a}$时，y取得最小值$\\frac{4ac-{b}^{2}}{4a}$，即顶点是抛物线的最低点．<br />②当a＜0时，抛物线y=ax<SUP>2</SUP>+bx+c（a≠0）的开口向下，x＜-$\\frac{b}{2a}$时，y随x的增大而增大；x＞-$\\frac{b}{2a}$时，y随x的增大而减小；x=-$\\frac{b}{2a}$时，y取得最大值$\\frac{4ac-{b}^{2}}{4a}$，即顶点是抛物线的最高点．<br />③抛物线y=ax<SUP>2</SUP>+bx+c（a≠0）的图象可由抛物线y=ax<SUP>2</SUP>的图象向右或向左（右）平移|-$\\frac{b}{2a}$|个单位，再向上或向下平移|$\\frac{4ac-{b}^{2}}{4a}$|个单位得到的．","Level1":"3","Level2":"H","AFlag":true,"BFlag":false,"APrice":2.00,"BPrice":0.40,"CPrice":0.30,"Rank":2,"Levels":null,"NW":0,"Score":0.0,"Count":0,"Seqs":null,"Subject":0,"Seq":0,"MData":null},"Subject":0},{"QuesID":"d7f7f5ba-3d16-417d-b583-060c66aab80f","PointNo":"K6","Major":false,"Point":{"No":"K6","Name":"三角形三边关系","Desc":"（1）三角形三边关系定理：三角形两边之和大于第三边．<BR>（2）在运用三角形三边关系判定三条线段能否构成三角形时并不一定要列出三个不等式，只要两条较短的线段长度之和大于第三条线段的长度即可判定这三条线段能构成一个三角形．<BR>（3）三角形的两边差小于第三边．<BR>（4）在涉及三角形的边长或周长的计算时，注意最后要用三边关系去检验，这是一个隐藏的定时炸弹，容易忽略．","Level1":"4","Level2":"K","AFlag":true,"BFlag":false,"APrice":2.00,"BPrice":0.40,"CPrice":0.30,"Rank":2,"Levels":null,"NW":0,"Score":0.0,"Count":0,"Seqs":null,"Subject":0,"Seq":0,"MData":null},"Subject":0}],"QuesPoint2s":[],"QuesTopics":[],"QuesGroups":[],"QuesFiles":[],"QuesChilds":[],"Subject":20,"Seq":0,"Score":0.0,"Other":0,"CateName":"选择题","Teacher":"曹先生老师","UserAnswers":[],"UserScores":[],"IsTrue":9,"Points":[{"Key":"H3","Value":"二次函数的性质"},{"Key":"K6","Value":"三角形三边关系"}],"Topics":[],"Options":["3","4","5","6"],"Answers":["2"],"Star":"☆☆☆☆☆","Point":0,"FavTime":122,"ViewCount":2439,"DownCount":86,"RealCount":2,"PaperCount":2032,"ParentID":null,"ParentContent":null,"LabelReportID":"7fc5ab2c-38c4-49f7-aece-29a44f57704e"}