2025年1月山东统考压轴题

[br][br]在平面直角坐标系[img width=29,height=20]data:image/wmf;base64,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[/img]中,已知抛物线[img width=132,height=39]data:image/wmf;base64,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[/img].[br][br][br](1)当[img width=31,height=17]data:image/wmf;base64,R0lGODlhJwAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABQAiAAsAhAAAAAAAAB0AAAAAHR0AHQAAMwAcSAAzWh4zRx1GbDIdADVIWzNbgEgcAFozAFtINUhbSEhbbkhuW0huf11/f1luf2xGHW5bNX9uSH9/XWaIiIBbM4iIZgECAwECAwECAwVQICCOZGmegBUwaOuOTRC8tCuwpRIkgFGjAtNgNPuZMDfScEQwOWRQ2eEUhJUKRioOgLVmTVWRT6TakqLQExJn6T4AzW8pDNAhAJvBQk6UiUIAOw==[/img]时,[br][br][br]①求证:该抛物线的顶点不在第三象限;[br][br][br]②若[img width=12,height=17]data:image/wmf;base64,R0lGODlhDwAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABAAJAAwAhAAAAAAAAB0AHR0AAAAAHQAAMwAdMh0AMgAcSAAzWh1GbDMAADIdADNbgEgcAFozAF1dM1tINUhbbl1/f0huf2xGHW5bNX9uSH9/XX9uWWaIiIBbM4iIZgECAwECAwECAwUtIAA8QSGeYoWiTrOKwisi0BCsxkmcC9oDm1VMlDhVECKHzwU4nBiKU8QGkJxCADs=[/img]为自然数,且该抛物线与[img width=12,height=13]data:image/wmf;base64,R0lGODlhDwAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwAKAAgAhAAAAAAAAB0AABwcHAAAHQAAMx0AMgAdMgAcSAAzWh1GbDMAADIAMjVbbjNbgEgcAFozAFtIHVtISEhZf11/f0huf2xGHW5bNW5bSG5GRn9uSH9/XWaIiIBbM4iIZgECAwUeIAAEhXgJiChCAKa+wADPNLDUEpDUgAETqgegIgoBADs=[/img]轴有两个不同交点[img width=20,height=21]data:image/wmf;base64,R0lGODlhGQAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABgASABAAhQAAAAAAAB0AAB0AHRwcHAAAHQAAMx0AMgAdMgAcSAAzWh1GbDMAADIAMjVbbjNbgEgcAEceM1ozAFtIHVtISEhZf11/f0huf1l/bmxGHW5bNW5bSG5GRn9/XX9uSGaIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZIQIAQIBkaj0YIcjksMpegJxOyOAYMQ0HCyFgWN8sBk8AsSMPM7lJ9pAAUQ6xQedQID8PIMGo0z/NGTmdHdE96RxlSh4NDAUJBADs=[/img],[img width=17,height=20]data:image/wmf;base64,R0lGODlhFQAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABAAOABEAhAAAAAAAAB0AAAAAHQAdMgAAMx0AMgAcSAAzWh0zWh1GbDIdADMAADVbbjNbgEgcAFozAFozHVluf11/f0huf2xGHW5GM25bNX9uWX9/XX9uSGaIiIBbM4iIZgECAwECAwVOICCOY0OOS0CMj3Iy5lWQDnmMEDIaI3POIshIcBrYRESSUcQZUADJ0RJJVY40ghrDJaoAq0KSjukU+URf0Q2lOoVPcB4czp2PEnaSaRQCADs=[/img]和[img width=21,height=21]data:image/wmf;base64,R0lGODlhGgAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABgATABAAhQAAAAAAAB0AAB0AHRwcHAAAHQAAMx0AMgAdMgAcSAAzWh1GbDMAADIAHTIAMjMzWzVbbjNbgEgcAFozAFozHVtIHVtISE5GRkhZf0ZGbl1/f0huf2xGHW5bNW5bSG5GRn9/XX9uSGaIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZLQIAQMBkaj0cJcmksMpmj51OyOAYMQ0HiyFgWPcwBk/AsSMPMbnppASiGjEAVoDx2hIdjQxg1moV1QxRDTmdIgYZGHGdziUIBkABBADs=[/img],[img width=64,height=21]data:image/wmf;base64,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[/img],求[img width=40,height=21]data:image/wmf;base64,R0lGODlhMgAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMACgAsAAwAhQAAAAAAAB0AABwcHAAAHQAAMx0AMgAdMgAcSAAzWh1GbDMAADIAHTIAMjMzWzVbbjNbgEgcAEceM1ozAFozHVtIHVtISE5GRkhZf0ZGbl1/f0huf1l/bmxGHW5bNW5bSG5GRn9uSH9/XWaIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZeQAAgUBACBAijcslsEo1I5gTwaVqvy2n1OsB6sd2veBIomwMJcXOhbgvZVwsg/Q4o3E05HVBkGoQXQgx4Vn9MBEYRABtGFIRGiEKKjBKPlkqVl5eZXxmahGafTAFCQQA7[/img]的值.[br][br][br](2)若[img width=32,height=17]data:image/wmf;base64,R0lGODlhKAAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABAAjAAwAhQAAAAAAAB0AAB0AHQAAHQAAMwAdMh0dNB0AMgAcSAAzWh4zRx1GbDMAADIdADQdHTMzSDVbbjNbgEgcAFozAF1dM1tINUhbbl1/f0huf1luf2xGHW5bNW5bSH9/XX9uSG5uWX9uWWaIiIBbM4iIZgECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZvQACAEigIj8ikcqncMJ/MRlE5kUCvQsHRiBxgj50lJalAJiqCwNURTXKFhiNhCQIsnlrkXNhA9pMOd1BeekIjSYRyX4lCewBlQhsJSg4HV3+RXBN+VkoggU9jSJAIRw4Ma4JKiW8WaQAXX2FMaW9BADs=[/img],直线[img width=64,height=17]data:image/wmf;base64,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[/img]与该抛物线有两个交点[img width=15,height=16]data:image/wmf;base64,R0lGODlhEwAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABQANAAwAhAAAAAAAAAAAHR0AHR0AAAAAMx0AMgAcSB0dSB0zWgAzWh1GbDMAADQ0HTNGbjNbgEgcAEgdHVozHVozAEhuf11/f2xGHW5bNW5GM39uSH9/XWaIiIBbM4iIZgECAwECAwUvICCOZGkC2UCdpMCOTfECCXC8CDC9kQgpp0lgGJiJGItSpkQwGUiY4ogwHDGItxAAOw==[/img],[img width=15,height=16]data:image/wmf;base64,R0lGODlhEwAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABQAMAAwAhAAAAAAAAAAdHQAAHR0AABwcHAAAMwAdMgAcSAAzWh0zWh1GbDMAADVbbjNbgEgcAFozAEczHkhuf11/f1luf2xGHW5bNX9uSH9/XX9uWWaIiIBbM4iIZgECAwECAwECAwU2ICACQVkKzTgOIxQ4amWoRKICtri9KkMrqgvBdBshRozD7XEL3HyqQE7EiqoeR1HEOTKZCqoQADs=[/img],其坐标分别为[img width=67,height=20]data:image/wmf;base64,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[/img]和[img width=44,height=20]data:image/wmf;base64,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[/img].当[img width=57,height=19]data:image/wmf;base64,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[/img]时,求[img width=132,height=39]data:image/wmf;base64,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[/img]的最小值.[br][br][br]
对于第一问,应该如何思考?拖动下面geogebra文件滑动条。并思考解决方案
对于第二问,你看到条件会想到什么?动手操作GGB,并思考思路,如有不清楚观看后面视频
通过本题,你对于解决此类问题有什么看法?
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Information: 2025年1月山东统考压轴题