Änderungen von Dokument BPE 8.4 Darstellungsformen, Achsenschnittpunkte

Zusammenfassung

• Seiteneigenschaften (1 geändert, 0 hinzugefügt, 0 gelöscht)
• Anhänge (0 geändert, 1 hinzugefügt, 0 gelöscht)
  • 8.4 - A4.svg

Details

Seiteneigenschaften

Inhalt

...	...	@@ -36,7 +36,7 @@
36	36
37	37	{{/aufgabe}}
38	38
39		-{{aufgabe id="Darstellungsformen quadratischer Funktionen" afb="II" kompetenzen="" quelle="S. Hochrein" zeit="" cc="by-sa" tags=""}}
	39	+{{aufgabe id="Darstellungsformen quadratischer Funktionen" afb="II" kompetenzen="K4, K5" quelle="S. Hochrein" zeit="3" cc="by-sa" tags=""}}
40	40	Die Funktionsgleichung einer quadratischen Funktion kann auf drei verschiedene Arten dargestellt werden:
41	41	(% class="border" %)
42	42	|Scheitelform|{{formula}}f(x)=a\cdot(x-x_S)^2+y_S{{/formula}}
...	...	@@ -49,5 +49,20 @@
49	49
50	50	{{/aufgabe}}
51	51
	52	+{{aufgabe id="" afb="" kompetenzen="" quelle="" zeit="" cc="by-sa" tags=""}}
	53	+Je nach Art der gegebenen Informationen ist die Scheitelform oder die Linearfaktorform besonders geeignet zum Aufstellen der Funktionsgleichung.
	54	+Begründe jeweils, welche Form bei den im Folgenden gegebenen Informationen zum Aufstellen der Funktionsgleichung geeignet ist.
	55	+
	56	+1. Der Graph der Funktion schneidet die x-Achse bei {{formula}}-3{{/formula}} und {{formula}}2{{/formula}} und die y-Achse bei {{formula}}-3{{/formula}}.
	57	+1. Der Scheitel der Funktion liegt bei {{formula}}S(2|4){{/formula}}, der Streckfaktor ist {{formula}}a=-2{{/formula}}.
	58	+1. Der Scheitel liegt bei {{formula}}S(3|1){{/formula}}, der Punkt {{formula}}A(5|2){{/formula}} liegt auf dem Graphen der Funktion.
	59	+1. Der Graph der Funktion hat sein Maximum bei {{formula}}S(0|2){{/formula}}, er schneidet die x-Achse bei {{formula}}x_1=3{{/formula}}.
	60	+1. (((Folgende Wertetabelle gehört zur Funktion.
	61	+(% class="border" style="table-layout: fixed; text-align:center" %)
	62	+|{{formula}}x{{/formula}}|0|1|2|3|4
	63	+|{{formula}}f(x){{/formula}}|5|3,5|3|3,5|5)))
	64	+1. Der Graph der Funktion ist in folgender Abbildung dargestellt.
	65	+{{/aufgabe}}
	66	+
52	52	{{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
53	53

8.4 - A4.svg

Author

...	...	@@ -1,0 +1,1 @@
	1	+XWiki.simonehochrein

Größe

...	...	@@ -1,0 +1,1 @@
	1	+16.4 KB

Inhalt

...	...	@@ -1,0 +1,1 @@
	1	+<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="1200" height="932"><defs><clipPath id="pkwUXBgKyNDa"><path fill="none" stroke="none" d=" M 0 0 L 1200 0 L 1200 932 L 0 932 L 0 0 Z"/></clipPath></defs><g transform="scale(1,1)" clip-path="url(#pkwUXBgKyNDa)"><g><rect fill="rgb(255,255,255)" stroke="none" x="0" y="0" width="1201" height="932" fill-opacity="1"/><path fill="none" stroke="rgb(180,179,186)" paint-order="fill stroke markers" d=" M 0.5 0.5 L 0.5 932.5 M 0.5 0.5 L 0.5 932.5 M 146.5 0.5 L 146.5 932.5 M 293.5 0.5 L 293.5 932.5 M 587.5 0.5 L 587.5 932.5 M 734.5 0.5 L 734.5 932.5 M 881.5 0.5 L 881.5 932.5 M 1028.5 0.5 L 1028.5 932.5 M 1175.5 0.5 L 1175.5 932.5" stroke-opacity="1" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10"/><path fill="none" stroke="rgb(180,179,186)" paint-order="fill stroke markers" d=" M 29.5 0.5 L 29.5 932.5 M 58.5 0.5 L 58.5 932.5 M 88.5 0.5 L 88.5 932.5 M 117.5 0.5 L 117.5 932.5 M 176.5 0.5 L 176.5 932.5 M 205.5 0.5 L 205.5 932.5 M 235.5 0.5 L 235.5 932.5 M 264.5 0.5 L 264.5 932.5 M 323.5 0.5 L 323.5 932.5 M 352.5 0.5 L 352.5 932.5 M 382.5 0.5 L 382.5 932.5 M 411.5 0.5 L 411.5 932.5 M 470.5 0.5 L 470.5 932.5 M 499.5 0.5 L 499.5 932.5 M 529.5 0.5 L 529.5 932.5 M 558.5 0.5 L 558.5 932.5 M 617.5 0.5 L 617.5 932.5 M 646.5 0.5 L 646.5 932.5 M 676.5 0.5 L 676.5 932.5 M 705.5 0.5 L 705.5 932.5 M 764.5 0.5 L 764.5 932.5 M 793.5 0.5 L 793.5 932.5 M 823.5 0.5 L 823.5 932.5 M 852.5 0.5 L 852.5 932.5 M 911.5 0.5 L 911.5 932.5 M 940.5 0.5 L 940.5 932.5 M 970.5 0.5 L 970.5 932.5 M 999.5 0.5 L 999.5 932.5 M 1058.5 0.5 L 1058.5 932.5 M 1087.5 0.5 L 1087.5 932.5 M 1116.5 0.5 L 1116.5 932.5 M 1146.5 0.5 L 1146.5 932.5" stroke-opacity="0.23529411764705882" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10"/><path fill="none" stroke="rgb(180,179,186)" paint-order="fill stroke markers" d=" M 0.5 84.5 L 1200.5 84.5 M 0.5 84.5 L 1200.5 84.5 M 0.5 231.5 L 1200.5 231.5 M 0.5 524.5 L 1200.5 524.5 M 0.5 671.5 L 1200.5 671.5 M 0.5 818.5 L 1200.5 818.5" stroke-opacity="1" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10"/><path fill="none" stroke="rgb(180,179,186)" paint-order="fill stroke markers" d=" M 0.5 25.5 L 1200.5 25.5 M 0.5 25.5 L 1200.5 25.5 M 0.5 54.5 L 1200.5 54.5 M 0.5 113.5 L 1200.5 113.5 M 0.5 142.5 L 1200.5 142.5 M 0.5 172.5 L 1200.5 172.5 M 0.5 201.5 L 1200.5 201.5 M 0.5 260.5 L 1200.5 260.5 M 0.5 289.5 L 1200.5 289.5 M 0.5 319.5 L 1200.5 319.5 M 0.5 348.5 L 1200.5 348.5 M 0.5 407.5 L 1200.5 407.5 M 0.5 436.5 L 1200.5 436.5 M 0.5 466.5 L 1200.5 466.5 M 0.5 495.5 L 1200.5 495.5 M 0.5 554.5 L 1200.5 554.5 M 0.5 583.5 L 1200.5 583.5 M 0.5 613.5 L 1200.5 613.5 M 0.5 642.5 L 1200.5 642.5 M 0.5 701.5 L 1200.5 701.5 M 0.5 730.5 L 1200.5 730.5 M 0.5 760.5 L 1200.5 760.5 M 0.5 789.5 L 1200.5 789.5 M 0.5 848.5 L 1200.5 848.5 M 0.5 877.5 L 1200.5 877.5 M 0.5 907.5 L 1200.5 907.5" stroke-opacity="0.23529411764705882" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10"/><path fill="none" stroke="rgb(28,28,31)" paint-order="fill stroke markers" d=" M 440.5 2.5 L 440.5 932.5" stroke-opacity="1" stroke-miterlimit="10"/><path fill="none" stroke="rgb(28,28,31)" paint-order="fill stroke markers" d=" M 440.5 1.5 L 432.5 9.5" stroke-opacity="1" stroke-miterlimit="10"/><path fill="none" stroke="rgb(28,28,31)" paint-order="fill stroke markers" d=" M 440.5 1.5 L 448.5 9.5" stroke-opacity="1" stroke-miterlimit="10"/><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="32px" font-style="normal" font-weight="normal" text-decoration="normal" x="1174" y="373" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">x</text><path fill="none" stroke="rgb(28,28,31)" paint-order="fill stroke markers" d=" M 0.5 377.5 L 1198.5 377.5" stroke-opacity="1" stroke-miterlimit="10"/><path fill="none" stroke="rgb(28,28,31)" paint-order="fill stroke markers" d=" M 1199.5 377.5 L 1191.5 369.5" stroke-opacity="1" stroke-miterlimit="10"/><path fill="none" stroke="rgb(28,28,31)" paint-order="fill stroke markers" d=" M 1199.5 377.5 L 1191.5 385.5" stroke-opacity="1" stroke-miterlimit="10"/><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="24px" font-style="normal" font-weight="normal" text-decoration="normal" x="135" y="405" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–2</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="24px" font-style="normal" font-weight="normal" text-decoration="normal" x="282" y="405" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–1</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="24px" font-style="normal" font-weight="normal" text-decoration="normal" x="582" y="405" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">1</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="24px" font-style="normal" font-weight="normal" text-decoration="normal" x="729" y="405" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">2</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="24px" font-style="normal" font-weight="normal" text-decoration="normal" x="876" y="405" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">3</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="24px" font-style="normal" font-weight="normal" text-decoration="normal" x="1023" y="405" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">4</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="24px" font-style="normal" font-weight="normal" text-decoration="normal" x="1170" y="405" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">5</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="32px" font-style="normal" font-weight="normal" text-decoration="normal" x="445" y="29" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">y</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="24px" font-style="normal" font-weight="normal" text-decoration="normal" x="403" y="829" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–3</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="24px" font-style="normal" font-weight="normal" text-decoration="normal" x="403" y="682" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–2</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="24px" font-style="normal" font-weight="normal" text-decoration="normal" x="403" y="535" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">–1</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="24px" font-style="normal" font-weight="normal" text-decoration="normal" x="417" y="242" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">1</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="24px" font-style="normal" font-weight="normal" text-decoration="normal" x="417" y="95" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">2</text><text fill="rgb(28,28,31)" stroke="none" font-family="geogebra-sans-serif, sans-serif" font-size="24px" font-style="normal" font-weight="normal" text-decoration="normal" x="417" y="405" text-anchor="start" dominant-baseline="alphabetic" fill-opacity="1">0</text><path fill="none" stroke="rgb(211,47,47)" paint-order="fill stroke markers" d=" M 161.71875 -12.09944618045148 L 164.0625 -4.149973735011599 L 166.40625 3.7621218866098616 L 168.75 11.636840684413073 L 171.09375 19.474182658397808 L 173.4375 27.27414780856435 L 175.78125 35.03673613491242 L 178.125 42.76194763744229 L 180.46875 50.44978231615397 L 182.8125 58.100240171047346 L 185.15625000000003 65.7133212021223 L 187.5 73.28902540937878 L 189.84375 80.82735279281701 L 192.18750000000003 88.32830335243705 L 194.53125 95.79187708823883 L 196.87500000000003 103.21807400022232 L 199.21875 110.60689408838743 L 201.5625 117.95833735273408 L 203.90625000000003 125.27240379326261 L 206.25 132.54909340997256 L 208.59375 139.78840620286445 L 210.93750000000003 146.99034217193804 L 213.28125 154.15490131719332 L 215.625 161.28208363863007 L 217.96875 168.3718891362487 L 220.3125 175.42431781004888 L 222.65625000000003 182.43936966003085 L 225 189.41704468619457 L 227.34375 196.35734288854 L 229.68750000000003 203.26026426706704 L 232.03125 210.12580882177562 L 234.37500000000003 216.9539765526661 L 236.71875 223.74476745973806 L 239.0625 230.49818154299186 L 241.40625000000003 237.21421880242738 L 243.75 243.8928792380446 L 246.09375 250.5341628498433 L 248.43750000000003 257.1380696378239 L 250.78125 263.704599601986 L 253.125 270.2337527423299 L 255.46875 276.7255290588556 L 257.8125 283.1799285515629 L 260.15625 289.59695122045196 L 262.5 295.97659706552247 L 264.84375 302.3188660867747 L 267.1875 308.62375828420875 L 269.53125 314.8912736578245 L 271.875 321.121412207622 L 274.21875 327.3141739336011 L 276.5625 333.4695588357618 L 278.90625 339.58756691410434 L 281.25 345.66819816862835 L 283.59375 351.7114525993343 L 285.9375 357.71733020622185 L 288.28125 363.6858309892911 L 290.625 369.6169549485419 L 292.96875 375.51070208397454 L 295.3125 381.3670723955889 L 297.65625 387.18606588338474 L 300 392.9676825473625 L 302.34375 398.7119223875219 L 304.6875 404.4187854038628 L 307.03125 410.0882715963856 L 309.375 415.72038096509004 L 311.71875 421.315113509976 L 314.0625 426.87246923104385 L 316.40625 432.3924481282934 L 318.75000000000006 437.8750502017246 L 321.09375 443.32027545133735 L 323.4375 448.7281238771319 L 325.78125 454.0985954791082 L 328.125 459.43169025726604 L 330.46875 464.7274082116057 L 332.8125 469.985749342127 L 335.15625 475.2067136488299 L 337.5 480.39030113171464 L 339.84375 485.53651179078105 L 342.1875 490.645345626029 L 344.53125 495.7168026374587 L 346.875 500.7508828250702 L 351.5625 510.706912728838 L 356.25 520.5134353373327 L 360.9375 530.1704506505541 L 365.625 539.6779586685022 L 370.3125 549.0359593911774 L 375 558.2444528185789 L 379.6875 567.3034389507072 L 384.375 576.2129177875624 L 389.0625 584.9728893291444 L 393.75000000000006 593.5833535754531 L 398.4375 602.0443105264885 L 403.125 610.3557601822506 L 407.8125 618.5177025427397 L 412.5 626.5301376079553 L 417.1875 634.3930653778978 L 421.875 642.106485852567 L 426.5625 649.6703990319629 L 431.25 657.0848049160854 L 435.9375 664.349703504935 L 440.625 671.4650947985111 L 445.3125 678.4309787968141 L 450 685.2473554998438 L 454.6875 691.9142249076002 L 459.375 698.4315870200835 L 464.0625 704.7994418372934 L 468.75000000000006 711.0177893592302 L 473.4375 717.0866295858937 L 478.125 723.0059625172838 L 482.8125 728.7757881534008 L 487.5 734.3961064942445 L 492.1875 739.866917539815 L 496.875 745.1882212901122 L 501.5625 750.3600177451361 L 506.25 755.3823069048868 L 510.9375 760.2550887693644 L 515.625 764.9783633385686 L 520.3125 769.5521306124996 L 525 773.9763905911573 L 529.6875 778.2511432745417 L 534.375 782.376388662653 L 539.0625 786.352126755491 L 543.75 790.1783575530558 L 548.4375 793.8550810553472 L 553.125 797.3822972623655 L 557.8125 800.7600061741105 L 562.5 803.9882077905822 L 567.1875 807.0669021117807 L 571.875 809.9960891377059 L 576.5625 812.775768868358 L 581.25 815.4059413037367 L 585.9375 817.8866064438422 L 590.625 820.2177642886745 L 595.3125 822.3994148382335 L 600 824.4315580925193 L 604.6875 826.3141940515318 L 609.375 828.0473227152711 L 614.0625 829.6309440837371 L 618.75 831.0650581569298 L 623.4375 832.3496649348494 L 628.125 833.4847644174956 L 632.8125 834.4703566048686 L 637.5 835.3064414969684 L 642.1875 835.9930190937949 L 646.875 836.5300893953483 L 651.5625 836.9176524016283 L 656.25 837.155708112635 L 660.9375 837.2442565283686 L 665.625 837.1832976488289 L 670.3125 836.972831474016 L 675 836.6128580039297 L 679.6875 836.1033772385703 L 684.375 835.4443891779376 L 689.0625 834.6358938220317 L 693.75 833.6778911708525 L 698.4375 832.5703812244001 L 703.125 831.3133639826743 L 707.8125 829.9068394456754 L 712.5 828.3508076134032 L 717.1875 826.6452684858577 L 721.875 824.790222063039 L 726.5625 822.7856683449471 L 731.25 820.631607331582 L 735.9375 818.3280390229436 L 740.625 815.8749634190318 L 745.3125 813.2723805198469 L 750 810.5202903253887 L 754.6875 807.6186928356574 L 759.375 804.5675880506526 L 764.0625 801.3669759703748 L 768.75 798.0168565948236 L 773.4375 794.5172299239991 L 778.125 790.8680959579015 L 782.8125 787.0694546965306 L 787.5 783.1213061398864 L 792.1875 779.0236502879691 L 796.875 774.7764871407783 L 801.5625 770.3798166983145 L 806.25 765.8336389605774 L 810.9375 761.137953927567 L 815.625 756.2927615992833 L 820.3125 751.2980619757265 L 825 746.1538550568963 L 829.6875 740.8601408427928 L 834.375 735.4169193334162 L 839.0625 729.8241905287664 L 843.75 724.0819544288431 L 848.4375 718.1902110336468 L 853.125 712.1489603431772 L 857.8125 705.9582023574344 L 862.5 699.6179370764183 L 867.1875 693.128164500129 L 871.875 686.4888846285662 L 876.5625 679.7000974617304 L 881.25 672.7618029996213 L 885.9375 665.6740012422389 L 890.625 658.4366921895833 L 895.3125 651.0498758416545 L 900 643.5135521984523 L 904.6875 635.8277212599769 L 909.375 627.9923830262285 L 914.0625 620.0075374972066 L 918.75 611.8731846729114 L 923.4375 603.5893245533432 L 928.125 595.1559571385014 L 932.8125 586.5730824283866 L 937.5 577.8407004229985 L 942.1875 568.9588111223372 L 946.875 559.9274145264026 L 951.5625 550.7465106351947 L 956.25 541.4160994487138 L 960.9375 531.9361809669593 L 965.625 522.3067551899317 L 970.3125 512.5278221176311 L 975 502.59938175005686 L 977.34375 497.57909633054237 L 979.6875 492.52143408720946 L 982.03125 487.4263950200583 L 984.375 482.2939791290891 L 986.71875 477.12418641430133 L 989.0625 471.9170168756952 L 991.40625 466.6724705132708 L 993.75 461.39054732702806 L 996.09375 456.071247316967 L 998.4375 450.7145704830879 L 1000.78125 445.32051682539026 L 1003.125 439.8890863438743 L 1005.46875 434.42027903854 L 1007.8125 428.91409490938736 L 1010.15625 423.37053395641647 L 1012.5 417.78959617962755 L 1014.84375 412.17128157902 L 1017.1875 406.5155901545941 L 1019.53125 400.82252190634995 L 1021.875 395.09207683428747 L 1024.21875 389.3242549384067 L 1026.5625 383.5190562187076 L 1028.90625 377.6764806751905 L 1031.25 371.7965283078547 L 1033.59375 365.8791991167007 L 1035.9375 359.92449310172833 L 1038.28125 353.93241026293765 L 1040.625 347.90295060032867 L 1042.96875 341.8361141139017 L 1045.3125 335.7319008036561 L 1047.65625 329.5903106695922 L 1050 323.41134371170995 L 1052.34375 317.19499993000943 L 1054.6875 310.94127932449055 L 1057.03125 304.6501818951534 L 1059.375 298.3217076419983 L 1061.71875 291.9558565650245 L 1064.0625 285.5526286642324 L 1066.40625 279.11202393962196 L 1068.75 272.63404239119325 L 1071.09375 266.11868401894617 L 1073.4375 259.5659488228812 L 1075.78125 252.97583680299755 L 1078.125 246.34834795929555 L 1080.46875 239.68348229177528 L 1082.8125 232.98123980043667 L 1085.15625 226.24162048527975 L 1087.5 219.4646243463045 L 1089.84375 212.65025138351135 L 1092.1875 205.7985015968995 L 1094.53125 198.90937498646937 L 1096.875 191.98287155222087 L 1099.21875 185.01899129415406 L 1101.5625 178.01773421226898 L 1103.90625 170.97910030656595 L 1106.25 163.90308957704423 L 1108.59375 156.7897020237042 L 1110.9375 149.63893764654586 L 1113.28125 142.45079644556918 L 1115.625 135.22527842077417 L 1117.96875 127.96238357216129 L 1120.3125 120.66211189972972 L 1122.65625 113.3244634034798 L 1125 105.94943808341156 L 1127.34375 98.53703593952503 L 1129.6875 91.08725697182018 L 1132.03125 83.60010118029703 L 1134.375 76.07556856495597 L 1136.71875 68.51365912579621 L 1139.0625 60.914372862818084 L 1141.40625 53.27770977602171 L 1143.75 45.60366986540697 L 1146.09375 37.89225313097393 L 1148.4375 30.14345957272303 L 1150.78125 22.357289190653375 L 1153.125 14.533741984765356 L 1155.46875 6.672817955059088 L 1157.8125 -1.2254828984654864 L 1160.15625 -9.16116057580848" stroke-opacity="0.6980392156862745" stroke-linecap="round" stroke-linejoin="round" stroke-miterlimit="10" stroke-width="2.5"/></g></g></svg>