Polynome aus Linearfaktoren Zeichnen

Mit dem Stift ein in Linearfaktoren gegebens Polynom qualitativ zeichen, dann die Zeichnung prüfen.

Neue Aufgaben sind möglich.

Polynome aus Linearfaktoren zeichnen

Ha 2014

Zeichne mit dem Stift einen qualitativen Graphen

Mit t kannst du prüfen.
Du brauchst von t nur das Vorzeichen zu wissen.

Schalte dann die Anzeige von f ein.

Neue Aufgabe

Lösche den Strich (Markieren Entf.)
Schalte die Anzeige von f aus.
Re-Maus auf f, Grundeinstellungen
f(x)=      löschen!!!!!!!!
Term beliebig verändern,
 t als Faktor lassen
Eigenschaftsfenster schließen.

t = -0.0015 (slider from -1 to 1, step 1.0E-4)
f(x) = (((t * (x + 4)^(2)) * (x - 3)) * (x - 8)^(2))
Strich1 = AttachCopyToView(PolyLine[(-5.100000000000002, 2.56), (-4.980000000000002, 2.28), (-4.960000000000002, 2.22), (-4.940000000000002, 2.16), (-4.920000000000002, 2.1), (-4.900000000000002, 2.04), (-4.880000000000002, 1.9800000000000002), (-4.860000000000002, 1.9200000000000002), (-4.840000000000002, 1.86), (-4.820000000000002, 1.8000000000000003), (-4.800000000000002, 1.7400000000000002), (-4.780000000000002, 1.6800000000000004), (-4.760000000000002, 1.6000000000000003), (-4.740000000000002, 1.5200000000000005), (-4.700000000000002, 1.4600000000000004), (-4.6800000000000015, 1.4000000000000004), (-4.660000000000002, 1.3400000000000005), (-4.620000000000002, 1.2800000000000005), (-4.600000000000001, 1.2200000000000004), (-4.580000000000002, 1.1600000000000006), (-4.540000000000002, 1.1000000000000005), (-4.520000000000001, 1.0400000000000007), (-4.500000000000002, 0.9800000000000006), (-4.480000000000001, 0.9200000000000007), (-4.460000000000002, 0.8600000000000007), (-4.460000000000002, 0.7800000000000007), (-4.440000000000001, 0.7200000000000008), (-4.420000000000002, 0.6600000000000008), (-4.400000000000001, 0.6000000000000009), (-4.380000000000002, 0.5400000000000008), (-4.360000000000001, 0.48000000000000087), (-4.320000000000001, 0.42000000000000093), (-4.300000000000002, 0.36000000000000093), (-4.260000000000002, 0.300000000000001), (-4.200000000000002, 0.24000000000000102), (-4.160000000000002, 0.18000000000000105), (-4.100000000000001, 0.12000000000000108), (-4.040000000000002, 0.0800000000000011), (-3.9800000000000013, 0.06000000000000111), (-3.9200000000000013, 0.04000000000000112), (-3.8400000000000016, 0.04000000000000112), (-3.7800000000000016, 0.06000000000000111), (-3.7200000000000015, 0.10000000000000109), (-3.6400000000000015, 0.12000000000000108), (-3.5800000000000014, 0.14000000000000107), (-3.5200000000000014, 0.16000000000000106), (-3.4600000000000013, 0.18000000000000105), (-3.4000000000000012, 0.20000000000000104), (-3.340000000000001, 0.22000000000000103), (-3.280000000000001, 0.260000000000001), (-3.220000000000001, 0.28000000000000097), (-3.160000000000001, 0.32000000000000095), (-3.100000000000001, 0.36000000000000093), (-3.040000000000001, 0.38000000000000095), (-2.9800000000000013, 0.42000000000000093), (-2.9200000000000013, 0.4600000000000009), (-2.860000000000001, 0.5000000000000009), (-2.800000000000001, 0.5600000000000008), (-2.740000000000001, 0.6000000000000009), (-2.700000000000001, 0.6600000000000008), (-2.640000000000001, 0.7000000000000007), (-2.580000000000001, 0.7600000000000008), (-2.520000000000001, 0.8000000000000007), (-2.460000000000001, 0.8400000000000007), (-2.400000000000001, 0.8800000000000007), (-2.3400000000000007, 0.9400000000000006), (-2.2800000000000007, 0.9800000000000006), (-2.2200000000000006, 1.0200000000000007), (-2.1600000000000006, 1.0800000000000005), (-2.100000000000001, 1.1200000000000006), (-2.040000000000001, 1.1600000000000006), (-1.9800000000000006, 1.2200000000000004), (-1.9000000000000008, 1.2800000000000005), (-1.8400000000000007, 1.3400000000000005), (-1.7800000000000007, 1.3800000000000003), (-1.7200000000000006, 1.4400000000000004), (-1.6600000000000006, 1.4800000000000004), (-1.6000000000000005, 1.5200000000000005), (-1.5400000000000005, 1.5600000000000003), (-1.4800000000000006, 1.6000000000000003), (-1.4200000000000006, 1.6400000000000003), (-1.3600000000000005, 1.6600000000000004), (-1.3000000000000005, 1.7000000000000002), (-1.2400000000000004, 1.7200000000000002), (-1.1800000000000004, 1.7400000000000002), (-1.1200000000000003, 1.7800000000000002), (-1.0600000000000005, 1.8000000000000003), (-1.0000000000000004, 1.8400000000000003), (-0.9200000000000004, 1.8800000000000001), (-0.8600000000000003, 1.9000000000000001), (-0.8000000000000003, 1.9200000000000002), (-0.7400000000000003, 1.9600000000000002), (-0.6800000000000003, 1.9800000000000002), (-0.6200000000000002, 2), (-0.5600000000000002, 2.04), (-0.5000000000000002, 2.06), (-0.44000000000000017, 2.1), (-0.36000000000000015, 2.12), (-0.3000000000000001, 2.16), (-0.22000000000000008, 2.18), (-0.16000000000000006, 2.2), (-0.10000000000000003, 2.22), (-0.040000000000000015, 2.24), (0.020000000000000007, 2.26), (0.08000000000000003, 2.28), (0.16000000000000006, 2.28), (0.2600000000000001, 2.3), (0.34000000000000014, 2.3), (0.42000000000000015, 2.3), (0.5000000000000002, 2.3), (0.5800000000000002, 2.3), (0.6600000000000003, 2.3), (0.7400000000000003, 2.3), (0.8200000000000003, 2.28), (0.9000000000000004, 2.28), (0.9600000000000004, 2.26), (1.0200000000000005, 2.24), (1.0800000000000003, 2.22), (1.1400000000000003, 2.2), (1.2200000000000004, 2.18), (1.2800000000000005, 2.16), (1.3400000000000005, 2.14), (1.4000000000000006, 2.1), (1.4600000000000006, 2.08), (1.5200000000000005, 2.02), (1.5800000000000005, 1.9800000000000002), (1.6400000000000006, 1.9200000000000002), (1.6800000000000006, 1.86), (1.7400000000000007, 1.8200000000000003), (1.8000000000000007, 1.7800000000000002), (1.8400000000000007, 1.7200000000000002), (1.9000000000000008, 1.6600000000000004), (1.9600000000000006, 1.6000000000000003), (2.020000000000001, 1.5400000000000003), (2.080000000000001, 1.4800000000000004), (2.1400000000000006, 1.4400000000000004), (2.1800000000000006, 1.3800000000000003), (2.2400000000000007, 1.3200000000000005), (2.3000000000000007, 1.2600000000000005), (2.3400000000000007, 1.2000000000000006), (2.380000000000001, 1.1400000000000006), (2.420000000000001, 1.0800000000000005), (2.460000000000001, 1.0200000000000007), (2.480000000000001, 0.9600000000000006), (2.520000000000001, 0.9000000000000007), (2.580000000000001, 0.8400000000000007), (2.620000000000001, 0.7800000000000007), (2.660000000000001, 0.7200000000000008), (2.680000000000001, 0.6600000000000008), (2.700000000000001, 0.6000000000000009), (2.720000000000001, 0.5400000000000008), (2.740000000000001, 0.48000000000000087), (2.760000000000001, 0.42000000000000093), (2.780000000000001, 0.36000000000000093), (2.800000000000001, 0.300000000000001), (2.820000000000001, 0.24000000000000102), (2.860000000000001, 0.18000000000000105), (2.9000000000000012, 0.12000000000000108), (2.9400000000000013, 0.06000000000000111), (2.9800000000000013, 1.1368683772161597E-15), (3.020000000000001, -0.05999999999999883), (3.040000000000001, -0.1199999999999988), (3.060000000000001, -0.17999999999999877), (3.080000000000001, -0.23999999999999874), (3.120000000000001, -0.2999999999999987), (3.160000000000001, -0.3599999999999987), (3.180000000000001, -0.41999999999999865), (3.200000000000001, -0.47999999999999865), (3.220000000000001, -0.5399999999999986), (3.240000000000001, -0.5999999999999985), (3.260000000000001, -0.6599999999999986), (3.280000000000001, -0.7199999999999985), (3.300000000000001, -0.7999999999999985), (3.320000000000001, -0.8599999999999984), (3.340000000000001, -0.9199999999999984), (3.360000000000001, -0.9799999999999984), (3.4000000000000012, -1.0399999999999983), (3.4400000000000013, -1.0999999999999983), (3.4800000000000013, -1.1599999999999984), (3.5000000000000013, -1.2199999999999982), (3.5600000000000014, -1.2799999999999983), (3.6000000000000014, -1.3399999999999983), (3.6400000000000015, -1.3999999999999981), (3.6800000000000015, -1.4599999999999982), (3.7200000000000015, -1.519999999999998), (3.7600000000000016, -1.579999999999998), (3.8000000000000016, -1.6399999999999981), (3.8200000000000016, -1.699999999999998), (3.860000000000001, -1.759999999999998), (3.9000000000000012, -1.8399999999999979), (3.9400000000000013, -1.899999999999998), (3.9800000000000013, -1.959999999999998), (4.020000000000001, -2.019999999999998), (4.080000000000002, -2.059999999999998), (4.1400000000000015, -2.119999999999998), (4.200000000000002, -2.139999999999998), (4.260000000000002, -2.179999999999998), (4.320000000000001, -2.199999999999998), (4.380000000000002, -2.219999999999998), (4.440000000000001, -2.2399999999999975), (4.500000000000002, -2.2599999999999976), (4.560000000000001, -2.2799999999999976), (4.6400000000000015, -2.2999999999999976), (4.7200000000000015, -2.2999999999999976), (4.780000000000002, -2.3199999999999976), (4.860000000000002, -2.3199999999999976), (4.940000000000002, -2.3199999999999976), (5.020000000000002, -2.3199999999999976), (5.100000000000002, -2.3199999999999976), (5.160000000000002, -2.2999999999999976), (5.240000000000002, -2.2999999999999976), (5.300000000000002, -2.2799999999999976), (5.360000000000002, -2.2599999999999976), (5.440000000000002, -2.2399999999999975), (5.500000000000002, -2.219999999999998), (5.560000000000002, -2.199999999999998), (5.620000000000002, -2.179999999999998), (5.680000000000002, -2.159999999999998), (5.740000000000002, -2.119999999999998), (5.8000000000000025, -2.079999999999998), (5.880000000000003, -2.039999999999998), (5.940000000000002, -1.9999999999999978), (6.000000000000002, -1.959999999999998), (6.060000000000002, -1.919999999999998), (6.140000000000002, -1.8599999999999979), (6.200000000000002, -1.799999999999998), (6.2600000000000025, -1.759999999999998), (6.320000000000002, -1.699999999999998), (6.360000000000002, -1.6399999999999981), (6.400000000000002, -1.579999999999998), (6.440000000000002, -1.519999999999998), (6.480000000000002, -1.4599999999999982), (6.500000000000003, -1.3999999999999981), (6.540000000000003, -1.3399999999999983), (6.580000000000003, -1.2799999999999983), (6.620000000000003, -1.2199999999999982), (6.640000000000002, -1.1599999999999984), (6.680000000000002, -1.0999999999999983), (6.700000000000003, -1.0399999999999983), (6.740000000000003, -0.9799999999999984), (6.780000000000003, -0.9199999999999984), (6.8400000000000025, -0.8599999999999984), (6.880000000000003, -0.7999999999999985), (6.920000000000003, -0.7399999999999985), (6.960000000000003, -0.6799999999999985), (7.020000000000002, -0.6199999999999986), (7.080000000000003, -0.5599999999999986), (7.140000000000002, -0.4999999999999986), (7.200000000000003, -0.45999999999999863), (7.240000000000003, -0.3999999999999987), (7.3000000000000025, -0.3599999999999987), (7.3400000000000025, -0.2999999999999987), (7.400000000000003, -0.27999999999999875), (7.460000000000003, -0.23999999999999874), (7.520000000000003, -0.19999999999999876), (7.580000000000003, -0.15999999999999878), (7.640000000000003, -0.1199999999999988), (7.700000000000003, -0.09999999999999881), (7.780000000000003, -0.09999999999999881), (7.8400000000000025, -0.07999999999999882), (7.900000000000003, -0.05999999999999883), (7.980000000000003, -0.05999999999999883), (8.060000000000002, -0.05999999999999883), (8.140000000000002, -0.05999999999999883), (8.220000000000002, -0.05999999999999883), (8.280000000000003, -0.07999999999999882), (8.360000000000003, -0.09999999999999881), (8.420000000000003, -0.1399999999999988), (8.480000000000004, -0.19999999999999876), (8.540000000000003, -0.23999999999999874), (8.600000000000003, -0.27999999999999875), (8.640000000000002, -0.3399999999999987), (8.700000000000003, -0.37999999999999867), (8.740000000000004, -0.43999999999999867), (8.760000000000003, -0.4999999999999986), (8.820000000000004, -0.5599999999999986), (8.860000000000003, -0.6199999999999986), (8.900000000000004, -0.6799999999999985), (8.940000000000003, -0.7399999999999985), (8.980000000000004, -0.7999999999999985), (9.020000000000003, -0.8599999999999984), (9.060000000000004, -0.9399999999999984), (9.080000000000004, -0.9999999999999983), (9.120000000000003, -1.0599999999999983), (9.140000000000004, -1.1199999999999983), (9.160000000000004, -1.1799999999999984), (9.180000000000003, -1.2399999999999982), (9.200000000000003, -1.2999999999999983), (9.200000000000003, -1.3799999999999981), (9.220000000000004, -1.4399999999999982), (9.240000000000004, -1.519999999999998), (9.260000000000003, -1.599999999999998), (9.280000000000003, -1.6599999999999981), (9.280000000000003, -1.739999999999998), (9.300000000000004, -1.819999999999998), (9.320000000000004, -1.899999999999998), (9.340000000000003, -1.979999999999998), (9.360000000000003, -2.039999999999998), (9.380000000000004, -2.119999999999998), (9.400000000000004, -2.179999999999998), (9.440000000000003, -2.2399999999999975), (9.460000000000003, -2.2999999999999976), (9.480000000000004, -2.3599999999999977), (9.500000000000004, -2.4199999999999977), (9.520000000000003, -2.4799999999999978), (9.540000000000003, -2.539999999999998), (9.560000000000004, -2.6199999999999974), (9.580000000000004, -2.6999999999999975), (9.600000000000003, -2.7799999999999976), (9.620000000000003, -2.8599999999999977), (9.620000000000003, -2.9399999999999973), (9.580000000000004, -2.9999999999999973), (9.540000000000003, -3.0599999999999974), (9.480000000000004, -3.0399999999999974), true], 1, (-5.780000000000002, -3.279999999999997), (13.520000000000005, 6.499999999999998), (0, 489), (965, 0))
Text1: "f(x) = " + f + ""
a = false
A = Point(xAxis)
B = Point(xAxis)
C = Point(xAxis)
D = Point(xAxis)
b = OrthogonalLine(A, xAxis)
c = OrthogonalLine(B, xAxis)
d = OrthogonalLine(C, xAxis)
e = OrthogonalLine(D, xAxis)
Strich2 = AttachCopyToView(PolyLine[(-4.900000000000002, -0.31999999999999756), (NaN, NaN), (-4.900000000000002, -0.31999999999999756), (-4.920000000000002, -0.2599999999999976), (-4.980000000000002, -0.31999999999999756), (-5.020000000000002, -0.37999999999999756), (-5.060000000000002, -0.4399999999999975), (-5.080000000000002, -0.4999999999999975), (-5.1400000000000015, -0.5799999999999974), (-5.1800000000000015, -0.6399999999999975), (-5.200000000000002, -0.6999999999999974), (-5.240000000000002, -0.7599999999999973), (NaN, NaN), (-4.520000000000001, -0.31999999999999756), (-4.800000000000002, -0.7799999999999974), (-4.860000000000002, -0.8799999999999973), (-4.900000000000002, -0.9399999999999973), (NaN, NaN), (-3.9400000000000013, -0.3399999999999976), (-4.080000000000002, -0.8399999999999973), (-4.1400000000000015, -0.8999999999999972), (-4.160000000000002, -0.9599999999999973), (NaN, NaN), (-3.4000000000000012, -0.35999999999999754), (-3.320000000000001, -0.7399999999999973), (-3.3800000000000012, -0.8999999999999972), (-3.4200000000000013, -0.9799999999999972), (-3.4400000000000013, -1.0599999999999972), (-3.4600000000000013, -1.1399999999999972), (-3.5000000000000013, -1.199999999999997), (-3.5400000000000014, -1.2799999999999971), (-3.4600000000000013, -1.239999999999997), (-3.360000000000001, -1.1399999999999972), (-3.320000000000001, -1.0799999999999972), (-3.260000000000001, -1.0199999999999971), (-3.200000000000001, -0.9599999999999973), (-3.140000000000001, -0.8999999999999972), (-3.080000000000001, -0.8599999999999973), (-3.020000000000001, -0.7999999999999974), (-2.9600000000000013, -0.7599999999999973), (-2.9000000000000012, -0.7199999999999974), (-2.840000000000001, -0.6999999999999974), (-2.760000000000001, -0.6399999999999975), (-2.680000000000001, -0.6199999999999974), (-2.620000000000001, -0.6399999999999975), (-2.640000000000001, -0.7199999999999974), (-2.680000000000001, -0.7999999999999974), (-2.700000000000001, -0.8599999999999973), (-2.740000000000001, -0.9199999999999973), (-2.780000000000001, -1.0199999999999971), (-2.820000000000001, -1.0799999999999972), (-2.860000000000001, -1.1599999999999973), (-2.800000000000001, -1.1199999999999972), (NaN, NaN), (-2.040000000000001, -0.4799999999999975), (-2.1800000000000006, -0.8599999999999973), (-2.2200000000000006, -0.9599999999999973), (-2.2600000000000007, -1.0399999999999971), (NaN, NaN), (-1.2600000000000005, -0.3999999999999975), (-1.4400000000000006, -0.8199999999999973), (-1.5000000000000004, -0.9599999999999973), (-1.5400000000000005, -1.0199999999999971), (-1.5800000000000005, -1.0799999999999972), (-1.6200000000000006, -1.1399999999999972), (-1.6600000000000006, -1.219999999999997), (-1.6200000000000006, -1.1599999999999973), (NaN, NaN), (-0.8000000000000003, -0.6399999999999975), (-0.9400000000000004, -1.0199999999999971), (-1.0000000000000004, -1.1199999999999972), (-1.0400000000000005, -1.199999999999997), (NaN, NaN), (-0.5400000000000001, -0.8399999999999973), (-0.6200000000000002, -1.2599999999999971), (-0.6200000000000002, -1.359999999999997), (-0.6400000000000002, -1.439999999999997), (-0.6800000000000003, -1.499999999999997), (NaN, NaN), (0.34000000000000014, -0.4399999999999975), (0.020000000000000007, -0.9199999999999973), (NaN, NaN), (0.6400000000000002, -0.37999999999999756), (0.4800000000000002, -0.7799999999999974), (0.44000000000000017, -0.8799999999999973), (0.42000000000000015, -0.9399999999999973), (0.3800000000000001, -1.0199999999999971), (0.36000000000000015, -1.0799999999999972), (NaN, NaN), (1.1600000000000004, -0.4999999999999975), (1.1200000000000003, -0.9199999999999973), (1.1000000000000003, -1.0399999999999971), (1.0800000000000003, -1.0999999999999972), (1.0600000000000005, -1.179999999999997), (1.0400000000000005, -1.239999999999997), (1.0800000000000003, -1.1399999999999972), (NaN, NaN), (1.7400000000000007, -0.5199999999999975), (1.6600000000000006, -0.9199999999999973), (1.6000000000000005, -1.0199999999999971), (1.5600000000000005, -1.0799999999999972), (NaN, NaN), (2.2000000000000006, -0.6999999999999974), (2.060000000000001, -1.1199999999999972), (NaN, NaN), (2.380000000000001, -0.6399999999999975), (2.2000000000000006, -1.0599999999999972), (2.1600000000000006, -1.179999999999997), (2.120000000000001, -1.239999999999997), (2.1400000000000006, -1.1599999999999973), (NaN, NaN), (3.9000000000000012, 1.3200000000000016), (3.6000000000000014, 0.22000000000000217), (3.5600000000000014, 0.1600000000000022), (NaN, NaN), (4.1400000000000015, 0.9800000000000018), (3.9200000000000013, 0.520000000000002), (3.860000000000001, 0.4000000000000021), (3.8400000000000016, 0.3200000000000021), (NaN, NaN), (4.900000000000002, 1.0800000000000016), (4.740000000000002, 0.540000000000002), (4.700000000000002, 0.4000000000000021), (4.660000000000002, 0.3400000000000021), (4.620000000000002, 0.2600000000000021), (4.560000000000001, 0.22000000000000217), (NaN, NaN), (5.100000000000002, 1.0800000000000016), (4.960000000000002, 0.5600000000000019), (4.920000000000002, 0.38000000000000206), (4.900000000000002, 0.28000000000000214), (4.880000000000002, 0.18000000000000219), (4.840000000000002, 0.08000000000000224), (4.820000000000002, -0.019999999999997718), (4.780000000000002, -0.09999999999999767), (4.760000000000002, -0.17999999999999763), (4.740000000000002, -0.2399999999999976), (NaN, NaN), (7.480000000000003, 1.3200000000000016), (NaN, NaN), (6.700000000000003, 1.0000000000000018), (6.440000000000002, 0.620000000000002), (6.380000000000003, 0.540000000000002), (6.360000000000002, 0.48000000000000204), (NaN, NaN), (6.8400000000000025, 0.8600000000000019), (6.700000000000003, 0.460000000000002), (6.660000000000003, 0.3200000000000021), (6.640000000000002, 0.2600000000000021), (6.620000000000003, 0.18000000000000219), (NaN, NaN), (7.3000000000000025, 0.9600000000000017), (7.080000000000003, 0.3400000000000021), (7.060000000000002, 0.28000000000000214), (7.000000000000003, 0.20000000000000218), (NaN, NaN), (7.500000000000003, 1.0400000000000018), (7.420000000000003, 0.540000000000002), (7.380000000000003, 0.3600000000000021), (7.360000000000003, 0.2600000000000021), (7.3400000000000025, 0.18000000000000219), (7.320000000000003, 0.08000000000000224), (NaN, NaN), (8.980000000000004, 1.2000000000000017), (8.720000000000002, 0.7200000000000019), (8.700000000000003, 0.6600000000000019), (8.680000000000003, 0.600000000000002), (NaN, NaN), (9.000000000000004, 0.8800000000000018), (8.860000000000003, 0.2600000000000021), (8.840000000000003, 0.10000000000000223), (8.820000000000004, 0.020000000000002262), (NaN, NaN), (9.540000000000003, 0.8800000000000018), (9.440000000000003, 0.48000000000000204), (9.360000000000003, 0.3200000000000021), (9.320000000000004, 0.22000000000000217), (9.280000000000003, 0.1400000000000022), (9.260000000000003, 0.060000000000002246), (9.220000000000004, -0.019999999999997718), (9.240000000000004, 0.060000000000002246), (NaN, NaN), (9.940000000000003, 0.8200000000000018), (9.760000000000003, 0.38000000000000206), (9.720000000000004, 0.3200000000000021), (9.660000000000004, 0.3400000000000021), (NaN, NaN), (10.260000000000003, 0.8200000000000018), (10.080000000000004, 0.42000000000000204), (10.040000000000004, 0.3600000000000021), (NaN, NaN), (10.580000000000004, 0.7800000000000019), (10.400000000000004, 0.3200000000000021), (10.340000000000003, 0.24000000000000216), (10.280000000000003, 0.22000000000000217), (NaN, NaN), (10.700000000000005, 0.7600000000000019), (10.500000000000004, 0.24000000000000216), (10.440000000000003, 0.1400000000000022), true], 1, (-5.780000000000002, -2.8399999999999963), (11.920000000000005, 6.499999999999999), (0, 467), (885, 0))