Quadratic Function Family

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2015-01-27 07:24

This example demonstrates the graphical changes of a quadratic function family. Key mathematical concepts include quadratic functions, parametric equations, and statistics involving variance and median. Using GeoGebra commands such as AttachCopyToView and Min, the parameters a, b, and c of the quadratic function can be dynamically adjusted to observe the changes in its graph. Suitable for high school mathematics education and learning about the properties of quadratic functions.

GeoGebra Commands & Parameters

AttachCopyToView(PolyLine[(1.5399999999999991, 1.96), (1.2599999999999993, 1.98), (1.0799999999999992, 1.98), (0.9599999999999993, 1.9000000000000001), (0.9199999999999993, 1.78), (0.9199999999999993, 1.7), (0.9599999999999993, 1.6400000000000001), (1.0599999999999992, 1.62), (1.2399999999999993, 1.62), (1.3599999999999992, 1.6600000000000001), (1.4199999999999993, 1.78), (1.4399999999999993, 1.86), (1.4599999999999993, 1.72), (1.5599999999999992, 1.58), (1.6599999999999993, 1.48), (NaN, NaN), (2.039999999999999, 2.08), (2.459999999999999, 2.04), (2.519999999999999, 1.94), (2.519999999999999, 1.78), (2.599999999999999, 1.6600000000000001), (2.699999999999999, 1.6), (NaN, NaN), (2.799999999999999, 2.08), (2.239999999999999, 1.6600000000000001), (2.119999999999999, 1.56), (NaN, NaN), (2.839999999999999, 2.94), (3.259999999999999, 2.82), (3.299999999999999, 2.7600000000000002), (3.039999999999999, 2.66), (2.899999999999999, 2.56), (2.879999999999999, 2.44), (3.079999999999999, 2.42), (NaN, NaN), (3.759999999999999, 2.18), (3.719999999999999, 1.74), (3.719999999999999, 1.62), (NaN, NaN), (3.9999999999999987, 2), (3.459999999999999, 1.98), (3.339999999999999, 1.98), (NaN, NaN), (4.679999999999999, 2.64), (4.579999999999998, 1.8800000000000001), (4.539999999999999, 1.76), (4.559999999999999, 1.82), (4.659999999999998, 1.92), (4.799999999999999, 2), (4.879999999999999, 2.02), (4.939999999999999, 1.98), (4.939999999999999, 1.84), (4.8199999999999985, 1.74), (4.659999999999998, 1.7), (4.559999999999999, 1.7), (4.499999999999999, 1.72), (NaN, NaN), (6.119999999999999, 2.16), (5.579999999999999, 1.68), (5.4799999999999995, 1.58), (NaN, NaN), (5.539999999999999, 2.08), (6.019999999999999, 1.6400000000000001), (NaN, NaN), (7.099999999999999, 2.24), (7.059999999999999, 1.68), (7.079999999999999, 1.62), (NaN, NaN), (7.559999999999999, 2.08), (7.059999999999999, 2.08), (6.8599999999999985, 2.08), (6.779999999999999, 2.08), (NaN, NaN), (8.639999999999999, 2.4), (8.219999999999999, 2.42), (8.1, 2.34), (8.059999999999999, 2.18), (8.059999999999999, 2.02), (8.28, 1.8800000000000001), (8.44, 1.86), (8.54, 1.84), true], 1, (-4.3, -7.6000000000000005), (11.939999999999998, 6.3), (0, 695), (812, 0)) → stroke1
Min(f, -10, 10) → B
AttachCopyToView(PolyLine[(-4.579999999999998, 2.5199999999999996), (-4.7799999999999985, 2.6399999999999997), (-4.839999999999998, 2.6599999999999997), (-4.959999999999998, 2.6199999999999997), (-4.959999999999998, 2.4399999999999995), (-4.959999999999998, 2.2199999999999998), (-4.959999999999998, 2.0199999999999996), (-4.959999999999998, 1.8599999999999997), (-4.979999999999999, 1.7399999999999998), (-4.999999999999998, 1.6799999999999997), (NaN, NaN), (-4.679999999999999, 2.0999999999999996), (-5.139999999999998, 2.0999999999999996), (-5.2799999999999985, 2.0999999999999996), (NaN, NaN), (-4.059999999999999, 2.6199999999999997), (-4.339999999999999, 2.4599999999999995), (-4.439999999999999, 2.28), (-4.459999999999998, 2.0799999999999996), (-4.459999999999998, 1.8599999999999997), (-4.379999999999999, 1.6999999999999997), (-4.2799999999999985, 1.5999999999999996), (NaN, NaN), (-3.799999999999999, 2.1599999999999997), (-4.099999999999999, 1.8399999999999996), (-4.159999999999998, 1.7399999999999998), (NaN, NaN), (-4.199999999999998, 2.1799999999999997), (-3.8999999999999986, 1.8599999999999997), (-3.779999999999999, 1.7599999999999998), (NaN, NaN), (-3.799999999999999, 2.6799999999999997), (-3.5599999999999987, 2.0599999999999996), (-3.4799999999999986, 1.7799999999999998), (-3.4799999999999986, 1.5599999999999998), (-3.5199999999999987, 1.3999999999999997), (-3.5999999999999988, 1.3599999999999999), (NaN, NaN), (-2.2599999999999993, 1.8599999999999997), (-2.479999999999999, 1.8399999999999996), (-2.619999999999999, 1.8399999999999996), (-2.6999999999999993, 1.8399999999999996), (NaN, NaN), (-2.1799999999999993, 1.4999999999999998), (-2.6799999999999993, 1.5199999999999998), (-2.779999999999999, 1.4999999999999998), (NaN, NaN), (-0.7799999999999997, 0.8799999999999999), (-1.8199999999999994, 0.9799999999999999), (-1.6199999999999994, 1.0199999999999998), (-1.1999999999999995, 1.0199999999999998), (-0.9999999999999997, 1.0199999999999998), (-1.4399999999999995, 1.0199999999999998), (-1.7199999999999995, 1.0199999999999998), (-1.2799999999999996, 1.0199999999999998), (-1.0999999999999996, 1.0199999999999998), (-1.2399999999999995, 1.0199999999999998), (-1.6199999999999994, 1.0199999999999998), (-1.7999999999999994, 1.0199999999999998), (-1.3799999999999994, 0.9599999999999999), (-1.0599999999999996, 0.9199999999999998), (-0.9599999999999997, 0.9199999999999998), (-1.1199999999999997, 0.9199999999999998), (-1.5399999999999996, 0.9199999999999998), (-1.7999999999999994, 0.9199999999999998), (-1.8999999999999995, 0.9199999999999998), (-1.7399999999999993, 0.9199999999999998), (-1.3799999999999994, 0.9199999999999998), (-1.1399999999999997, 0.9199999999999998), (NaN, NaN), (3.659999999999999, 5.279999999999999), (3.9599999999999986, 5.199999999999999), (4.239999999999998, 5.199999999999999), (4.419999999999998, 5.199999999999999), (4.599999999999999, 5.199999999999999), (4.7799999999999985, 5.199999999999999), (4.959999999999998, 5.199999999999999), (5.099999999999999, 5.199999999999999), (5.179999999999998, 5.179999999999999), (5.299999999999998, 5.159999999999999), (5.419999999999998, 5.159999999999999), (5.499999999999998, 5.159999999999999), true], 1, (-6.839999999999998, -7.739999999999998), (9.399999999999997, 6.159999999999999), (8.548717289613705e-15, 698), (812, 3.0000000000000258)) → stroke2