顶点式抛物线族在 iPad 上的演示
几何画板及绘图内容加载中,请稍等……
①本范例演示了不同参数下顶点式抛物线族的变化规律;②涉及的核心数学概念包括抛物线方程、顶点坐标、参数影响、散点图等;③作图要点——使用了 GeoGebra 命令 AttachCopyToView 来展示对象 a, h, k, f, stroke1 的变化;④适合高中数学教学,用于理解抛物线参数与图像的关系,以及动态几何演示。
GeoGebra 命令及参数
AttachCopyToView(PolyLine[(-5.299999999999997, 3.3000000000000003), (-5.679999999999997, 3.4), (-5.739999999999997, 3.38), (-5.759999999999997, 3.2600000000000002), (-5.759999999999997, 3.14), (-5.739999999999997, 3.02), (-5.679999999999997, 2.9), (-5.659999999999997, 2.8000000000000003), (-5.659999999999997, 2.72), (NaN, NaN), (-5.479999999999997, 3.02), (-5.759999999999997, 2.98), (-5.859999999999997, 2.98), (NaN, NaN), (-4.939999999999997, 3.48), (-5.179999999999997, 3.14), (-5.179999999999997, 2.96), (-5.079999999999997, 2.7800000000000002), (-4.919999999999997, 2.68), (-4.819999999999998, 2.66), (NaN, NaN), (-4.859999999999998, 3.2600000000000002), (-4.7399999999999975, 3.22), (-4.639999999999997, 3.18), (-4.579999999999997, 3.06), (-4.519999999999998, 2.94), (-4.479999999999998, 2.82), (-4.439999999999998, 2.7600000000000002), (NaN, NaN), (-4.359999999999998, 3.24), (-4.619999999999997, 3.02), (-4.7399999999999975, 2.9), (-4.799999999999997, 2.82), (NaN, NaN), (-4.299999999999997, 3.58), (-4.179999999999998, 3), (-4.179999999999998, 2.72), (-4.339999999999997, 2.58), (-4.439999999999998, 2.48), (NaN, NaN), (-3.4799999999999978, 3.1), (-3.7199999999999975, 3.08), (-3.8799999999999977, 3.08), (-3.9599999999999977, 3.08), (NaN, NaN), (-3.3799999999999977, 2.86), (-3.7599999999999976, 2.8000000000000003), (-3.8799999999999977, 2.8000000000000003), (NaN, NaN), (-2.539999999999998, 3.06), (-2.699999999999998, 3.24), (-2.799999999999998, 3.24), (-2.899999999999998, 3.16), (-2.899999999999998, 3.06), (-2.899999999999998, 2.96), (-2.899999999999998, 2.86), (-2.899999999999998, 2.7600000000000002), (-2.839999999999998, 2.72), (-2.739999999999998, 2.72), (-2.639999999999998, 2.72), (-2.559999999999998, 2.7600000000000002), (-2.539999999999998, 2.84), (-2.539999999999998, 2.92), (-2.4999999999999982, 2.7600000000000002), (-2.459999999999998, 2.66), (NaN, NaN), (-1.8599999999999983, 3.94), (-2.0199999999999982, 3.66), (-2.1199999999999983, 3.42), (-2.1599999999999984, 3.16), (-2.1599999999999984, 2.9), (-2.1199999999999983, 2.66), (-2.0399999999999983, 2.46), (-1.9599999999999982, 2.38), (NaN, NaN), (-1.2799999999999985, 3.18), (-1.4199999999999984, 3.06), (-1.5399999999999983, 2.96), (-1.5999999999999983, 2.86), (-1.6799999999999984, 2.8000000000000003), (NaN, NaN), (-1.7399999999999982, 3.14), (-1.6799999999999984, 3.1), (-1.5599999999999983, 3.06), (-1.4199999999999984, 2.96), (-1.3199999999999985, 2.9), (NaN, NaN), (-0.8199999999999986, 2.98), (-0.9799999999999985, 2.96), (NaN, NaN), (-0.4799999999999987, 3.5), (-0.4999999999999987, 3.42), (-0.4599999999999987, 3.22), (-0.4199999999999987, 2.98), (-0.3799999999999987, 2.8000000000000003), (-0.35999999999999877, 2.72), (-0.3199999999999988, 2.82), (-0.2399999999999988, 2.98), (-0.13999999999999882, 2.98), (-0.07999999999999884, 2.86), (-0.059999999999998846, 2.7600000000000002), (-0.059999999999998846, 2.66), (NaN, NaN), (0.02000000000000113, 3.7), (0.060000000000001115, 3.6), (0.20000000000000107, 3.46), (0.30000000000000104, 3.22), (0.36000000000000104, 2.98), (0.36000000000000104, 2.72), (0.320000000000001, 2.52), (0.22000000000000106, 2.4), (0.16000000000000109, 2.38), (NaN, NaN), (0.26000000000000106, 3.88), (0.320000000000001, 3.9), (0.46000000000000096, 3.9), (0.5400000000000009, 3.86), (0.5600000000000009, 3.8000000000000003), (0.500000000000001, 3.74), (0.420000000000001, 3.68), (0.580000000000001, 3.62), (0.700000000000001, 3.58), (NaN, NaN), (0.9600000000000009, 3.14), (0.9400000000000008, 3.08), (0.9400000000000008, 2.9), (0.9600000000000009, 2.7600000000000002), (0.9800000000000009, 2.68), (NaN, NaN), (1.2000000000000008, 2.9), (0.7800000000000009, 2.9), (0.6800000000000009, 2.9), (NaN, NaN), (1.5000000000000007, 3.2800000000000002), (1.5400000000000007, 2.86), (1.5600000000000007, 2.66), (1.5600000000000007, 2.52), (NaN, NaN), (1.8400000000000005, 2.94), (1.7200000000000006, 2.9), (1.6200000000000006, 2.9), (1.6400000000000006, 2.84), (1.7200000000000006, 2.8000000000000003), (1.8600000000000005, 2.7), (1.9800000000000004, 2.6), (2.1000000000000005, 2.52), (2.1600000000000006, 2.48), (NaN, NaN), (-5.979999999999997, 6.3), (-6.239999999999997, 5.96), (-6.299999999999997, 5.74), (-6.299999999999997, 5.58), (-6.279999999999997, 5.46), (-6.199999999999997, 5.42), (-6.1199999999999966, 5.4), (-6.059999999999997, 5.38), (NaN, NaN), (-5.739999999999997, 6.0200000000000005), (-5.739999999999997, 5.64), (-5.739999999999997, 5.5200000000000005), (-5.739999999999997, 5.44), (-5.679999999999997, 5.5200000000000005), (-5.619999999999997, 5.62), (-5.539999999999997, 5.68), (-5.459999999999997, 5.7), (-5.379999999999997, 5.66), (-5.379999999999997, 5.54), (-5.359999999999997, 5.44), (-5.339999999999997, 5.38), (NaN, NaN), (-4.899999999999998, 5.42), (-4.999999999999997, 5.0200000000000005), (NaN, NaN), (-4.459999999999997, 6.08), (-4.439999999999998, 5.68), (-4.439999999999998, 5.5), (-4.439999999999998, 5.36), (NaN, NaN), (-4.019999999999998, 5.92), (-4.279999999999998, 5.6000000000000005), (-4.1599999999999975, 5.5600000000000005), (-4.039999999999997, 5.5200000000000005), (-3.9799999999999978, 5.46), (NaN, NaN), (-3.6799999999999975, 6.12), (-3.2999999999999976, 5.62), (-3.3599999999999977, 5.42), (-3.559999999999998, 5.34), (NaN, NaN), (-5.979999999999997, 4.68), (-5.879999999999997, 4.38), (-5.839999999999997, 4.24), (-5.819999999999997, 4.16), (-5.739999999999997, 4.14), (-5.659999999999997, 4.28), (-5.579999999999997, 4.42), (-5.499999999999997, 4.5600000000000005), (-5.399999999999997, 4.68), (-5.319999999999997, 4.7), (NaN, NaN), (-5.119999999999997, 4.4), (-4.759999999999997, 4.38), (-4.619999999999997, 4.48), (-4.579999999999997, 4.58), (-4.599999999999997, 4.68), (-4.7399999999999975, 4.72), (-4.899999999999998, 4.72), (-4.999999999999997, 4.6000000000000005), (-5.039999999999997, 4.46), (-5.059999999999997, 4.32), (-4.979999999999997, 4.18), (-4.779999999999998, 4.12), (-4.599999999999997, 4.08), (-4.459999999999997, 4.08), (NaN, NaN), (-4.1599999999999975, 4.6000000000000005), (-4.139999999999998, 4.28), (-4.099999999999998, 4.2), (-4.059999999999998, 4.38), (-3.999999999999998, 4.5), (-3.9599999999999977, 4.5600000000000005), (-3.8599999999999977, 4.5600000000000005), (-3.7799999999999976, 4.5600000000000005), (NaN, NaN), (-3.3999999999999977, 5.04), (-3.4199999999999977, 4.94), (-3.499999999999998, 4.32), (NaN, NaN), (-3.099999999999998, 4.84), (-3.8399999999999976, 4.8), (-3.9199999999999977, 4.8), (NaN, NaN), (-3.199999999999998, 4.44), (-2.9599999999999977, 4.42), (-2.859999999999998, 4.42), (-2.819999999999998, 4.48), (-2.819999999999998, 4.5600000000000005), (-2.899999999999998, 4.62), (-3.019999999999998, 4.62), (-3.079999999999998, 4.54), (-3.079999999999998, 4.38), (-2.9399999999999977, 4.22), (-2.799999999999998, 4.16), (NaN, NaN), (-2.5199999999999982, 4.64), (-2.259999999999998, 4.36), (-2.1199999999999983, 4.24), (-1.9999999999999982, 4.14), (NaN, NaN), (-2.0199999999999982, 4.7), (-2.399999999999998, 4.48), (-2.5199999999999982, 4.36), (-2.619999999999998, 4.24), (-2.679999999999998, 4.14), (-2.719999999999998, 4.08), true], 1, (-6.6599999999999975, -7.26), (9.579999999999997, 6.640000000000001), (0, 695), (812, 0)) → stroke1