配方法可视化

几何画板及绘图内容加载中，请稍等……

2016-03-15 15:43

函数解析几何函数图像

该范例通过图形展示配方法，将抛物线与完全平方三项式“母函数”联系起来。使用GeoGebra命令如Min, Function, Point等进行构造。适合初中及以上学生学习二次函数的配方法。

GeoGebra 命令及参数

Min(t, 1) → t_1
Function({9.622135331408963, 23.587163892952123, 4.14497316841929, 4.14497316841929, 4.14497316841929, 4.14497316841929, 4.14497316841929, 4.151349893789858, 4.157726619160425, 4.164103344530993, 4.1704800699015605, 4.176856795272128, 4.176856795272128, 4.176856795272128, 4.176856795272128, 4.176856795272128, 4.187484670889741, 4.198112546507354, 4.208740422124967, 4.208740422124967, 4.208740422124967, 4.208740422124967, 4.208740422124967, 4.208740422124967, 4.229996173360192, 4.251251924595418, 4.272507675830643, 4.2831355514482565, 4.293763427065869, 4.304391302683482, 4.320333116109901, 4.336274929536319, 4.352216742962739, 4.368158556389158, 4.368158556389158, 4.368158556389158, 4.368158556389158, 4.368158556389158, 4.368158556389158, 4.378786432006771, 4.389414307624383, 4.400042183241996, 4.421297934477221, 4.442553685712447, 4.463809436947672, 4.474437312565285, 4.485065188182898, 4.495693063800511, 4.495693063800511, 4.495693063800511, 4.495693063800511, 4.495693063800511, 4.516948815035736, 4.538204566270962, 4.559460317506187, 4.570088193123801, 4.580716068741413, 4.591343944359026, 4.612599695594251, 4.633855446829476, 4.655111198064702, 4.655111198064702, 4.655111198064702, 4.655111198064702, 4.655111198064702, 4.655111198064702, 4.665739073682315, 4.676366949299928, 4.686994824917541, 4.686994824917541, 4.686994824917541, 4.686994824917541, 4.686994824917541, 4.708250576152767, 4.729506327387992, 4.750762078623217, 4.76138995424083, 4.772017829858442, 4.782645705476055, 4.782645705476055, 4.782645705476055, 4.782645705476055, 4.782645705476055, 4.782645705476055, 4.80390145671128, 4.825157207946506, 4.846412959181731, 4.942063839740246, 4.942063839740246, 4.942063839740246, 4.942063839740246, 4.942063839740246, 4.942063839740246, 4.952691715357859, 4.963319590975472, 4.973947466593085, 4.995203217828311, 5.016458969063536, 5.037714720298761, 5.048342595916374, 5.0589704715339865, 5.069598347151599, 5.090854098386825, 5.11210984962205, 5.133365600857276, 5.165249227710114, 5.197132854562953, 5.2290164814157905, 5.239644357033403, 5.2502722326510165, 5.260900108268629, 5.282155859503855, 5.30341161073908, 5.3246673619743055, 5.335295237591918, 5.345923113209531, 5.356550988827144, 5.377806740062369, 5.399062491297595, 5.4203182425328205, 5.5159691230913355, 5.526596998708949, 5.537224874326561, 5.547852749944173, 5.569108501179399, 5.5903642524146235, 5.61162000364985, 5.622247879267462, 5.632875754885075, 5.643503630502688, 5.691329070781945, 5.739154511061203, 5.760410262296428, 5.781666013531654, 5.80292176476688, 5.834805391619717, 5.866689018472556, 5.898572645325394, 5.930456272178232, 5.962339899031071, 5.994223525883909, 6.089874406442424, 6.100502282060037, 6.11113015767765, 6.121758033295262, 6.169583473574519, 6.2174089138537765, 6.249292540706615, 6.281176167559454, 6.3130597944122915, 6.4087106749708065, 6.440594301823644, 6.472477928676483, 6.504361555529321, 6.552186995808578, 6.600012436087836, 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10.234745897311397, 10.298513151017074, 10.521698538986941, 10.569523979266199, 10.617349419545457, 10.872418434368162, 10.920243874647419, 10.968069314926677, 11.191254702896545, 11.223138329749384, 11.25502195660222, 11.28690558345506, 11.414440090866412, 11.541974598277765, 11.63762547883628, 11.685450919115539, 11.733276359394795, 11.956461747364663, 11.988345374217502, 12.020229001070339, 12.052112627923178, 12.099938068202434, 12.147763508481692, 12.243414389040208, 12.291239829319466, 12.339065269598722, 12.434716150157236, 12.455971901392461, 12.477227652627688, 12.498483403862913, 12.546308844142171, 12.594134284421427, 12.604762160039039, 12.615390035656652, 12.626017911274266, 12.721668791832782, 12.742924543068007, 12.764180294303232, 12.785436045538457, 12.833261485817715, 12.881086926096973, 12.891714801714585, 12.902342677332198, 12.91297055294981, 13.008621433508326, 13.02987718474355, 13.051132935978776, 13.072388687214001, 13.083016562831615, 13.093644438449227, 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14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782, 14.889755417825782}) → g
Point(g) → D
Point(g) → E
Vector(V, B) → u
Polynomial((x - x(C))^(2) + y(C)) → f
Polynomial((x - x(V))^(2) + y(V)) → h_1
Max(t - 1, 0) → t_2
Vector(C, F) → v
Polynomial(h_1(x) - h_1(0)) → p
Max(t - 1, 0) → t_3
Textfield(gb) → InputBox1
Textfield(gc) → InputBox2