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",[573,1169,1171,1191],{"className":1170},[576],[573,1172,1174],{"className":1173},[580],[582,1175,1176],{"xmlns":584},[586,1177,1178,1188],{},[589,1179,1180,1182,1185],{},[592,1181,611],{},[596,1183,1184],{},">",[618,1186,1187],{},"0",[635,1189,1190],{"encoding":637},"a > 0",[573,1192,1194,1213],{"className":1193,"ariaHidden":643},[642],[573,1195,1197,1201,1204,1207,1210],{"className":1196},[647],[573,1198],{"className":1199,"style":1200},[651],"height:0.5782em;vertical-align:-0.0391em;",[573,1202,611],{"className":1203},[656,657],[573,1205],{"className":1206,"style":674},[673],[573,1208,1184],{"className":1209},[678],[573,1211],{"className":1212,"style":674},[673],[573,1214,1216,1220],{"className":1215},[647],[573,1217],{"className":1218,"style":1219},[651],"height:0.6444em;",[573,1221,1187],{"className":1222},[656]," ist der Scheitelpunkt der tiefste Punkt der Parabel, bei ",[573,1225,1227,1246],{"className":1226},[576],[573,1228,1230],{"className":1229},[580],[582,1231,1232],{"xmlns":584},[586,1233,1234,1243],{},[589,1235,1236,1238,1241],{},[592,1237,611],{},[596,1239,1240],{},"\u003C",[618,1242,1187],{},[635,1244,1245],{"encoding":637},"a \u003C 0",[573,1247,1249,1267],{"className":1248,"ariaHidden":643},[642],[573,1250,1252,1255,1258,1261,1264],{"className":1251},[647],[573,1253],{"className":1254,"style":1200},[651],[573,1256,611],{"className":1257},[656,657],[573,1259],{"className":1260,"style":674},[673],[573,1262,1240],{"className":1263},[678],[573,1265],{"className":1266,"style":674},[673],[573,1268,1270,1273],{"className":1269},[647],[573,1271],{"className":1272,"style":1219},[651],[573,1274,1187],{"className":1275},[656]," der höchste. Wer lieber eine fertige Formel für den y-Wert hat: ",[573,1278,1280,1319],{"className":1279},[576],[573,1281,1283],{"className":1282},[580],[582,1284,1285],{"xmlns":584},[586,1286,1287,1316],{},[589,1288,1289,1295,1297,1299,1301],{},[797,1290,1291,1293],{},[592,1292,1029],{},[592,1294,803],{},[596,1296,608],{},[592,1298,633],{},[596,1300,808],{},[810,1302,1303,1309],{},[613,1304,1305,1307],{},[592,1306,626],{},[618,1308,620],{},[589,1310,1311,1314],{},[618,1312,1313],{},"4",[592,1315,611],{},[635,1317,1318],{"encoding":637},"y_S = c - \\frac{b^2}{4a}",[573,1320,1322,1377,1396],{"className":1321,"ariaHidden":643},[642],[573,1323,1325,1328,1368,1371,1374],{"className":1324},[647],[573,1326],{"className":1327,"style":1058},[651],[573,1329,1331,1334],{"className":1330},[656],[573,1332,1029],{"className":1333,"style":1065},[656,657],[573,1335,1337],{"className":1336},[701],[573,1338,1340,1360],{"className":1339},[705,845],[573,1341,1343,1357],{"className":1342},[709],[573,1344,1346],{"className":1345,"style":852},[713],[573,1347,1348,1351],{"style":1080},[573,1349],{"className":1350,"style":722},[721],[573,1352,1354],{"className":1353},[726,727,728,729],[573,1355,803],{"className":1356,"style":865},[656,657,729],[573,1358,870],{"className":1359},[869],[573,1361,1363],{"className":1362},[709],[573,1364,1366],{"className":1365,"style":877},[713],[573,1367],{},[573,1369],{"className":1370,"style":674},[673],[573,1372,608],{"className":1373},[678],[573,1375],{"className":1376,"style":674},[673],[573,1378,1380,1384,1387,1390,1393],{"className":1379},[647],[573,1381],{"className":1382,"style":1383},[651],"height:0.6667em;vertical-align:-0.0833em;",[573,1385,633],{"className":1386},[656,657],[573,1388],{"className":1389,"style":736},[673],[573,1391,808],{"className":1392},[740],[573,1394],{"className":1395,"style":736},[673],[573,1397,1399,1403],{"className":1398},[647],[573,1400],{"className":1401,"style":1402},[651],"height:1.3629em;vertical-align:-0.345em;",[573,1404,1406,1409,1503],{"className":1405},[656],[573,1407],{"className":1408},[662,905],[573,1410,1412],{"className":1411},[810],[573,1413,1415,1495],{"className":1414},[705,845],[573,1416,1418,1492],{"className":1417},[709],[573,1419,1422,1439,1447],{"className":1420,"style":1421},[713],"height:1.0179em;",[573,1423,1424,1427],{"style":921},[573,1425],{"className":1426,"style":925},[721],[573,1428,1430],{"className":1429},[726,727,728,729],[573,1431,1433,1436],{"className":1432},[656,729],[573,1434,1313],{"className":1435},[656,729],[573,1437,611],{"className":1438},[656,657,729],[573,1440,1441,1444],{"style":940},[573,1442],{"className":1443,"style":925},[721],[573,1445],{"className":1446,"style":948},[947],[573,1448,1449,1452],{"style":951},[573,1450],{"className":1451,"style":925},[721],[573,1453,1455],{"className":1454},[726,727,728,729],[573,1456,1458],{"className":1457},[656,729],[573,1459,1461,1464],{"className":1460},[656,729],[573,1462,626],{"className":1463},[656,657,729],[573,1465,1467],{"className":1466},[701],[573,1468,1470],{"className":1469},[705],[573,1471,1473],{"className":1472},[709],[573,1474,1477],{"className":1475,"style":1476},[713],"height:0.8913em;",[573,1478,1480,1484],{"style":1479},"top:-2.931em;margin-right:0.0714em;",[573,1481],{"className":1482,"style":1483},[721],"height:2.5em;",[573,1485,1489],{"className":1486},[726,1487,1488,729],"reset-size3","size1",[573,1490,620],{"className":1491},[656,729],[573,1493,870],{"className":1494},[869],[573,1496,1498],{"className":1497},[709],[573,1499,1501],{"className":1500,"style":973},[713],[573,1502],{},[573,1504],{"className":1505},[669,905],[559,1507,1509],{"id":1508},"herleitung","Herleitung",[564,1511,1512,1513,1627,1628,1656,1657,1685,1686,1756],{},"Die Parabel ist symmetrisch, der Scheitelpunkt liegt also mittig zwischen zwei Punkten mit gleichem y-Wert. Die Parabel ",[573,1514,1516,1546],{"className":1515},[576],[573,1517,1519],{"className":1518},[580],[582,1520,1521],{"xmlns":584},[586,1522,1523,1543],{},[589,1524,1525,1527,1529,1531,1537,1539,1541],{},[592,1526,1029],{},[596,1528,608],{},[592,1530,611],{},[613,1532,1533,1535],{},[592,1534,602],{},[618,1536,620],{},[596,1538,623],{},[592,1540,626],{},[592,1542,602],{},[635,1544,1545],{"encoding":637},"y = ax^2 + bx",[573,1547,1549,1567,1614],{"className":1548,"ariaHidden":643},[642],[573,1550,1552,1555,1558,1561,1564],{"className":1551},[647],[573,1553],{"className":1554,"style":1058},[651],[573,1556,1029],{"className":1557,"style":1065},[656,657],[573,1559],{"className":1560,"style":674},[673],[573,1562,608],{"className":1563},[678],[573,1565],{"className":1566,"style":674},[673],[573,1568,1570,1573,1576,1605,1608,1611],{"className":1569},[647],[573,1571],{"className":1572,"style":688},[651],[573,1574,611],{"className":1575},[656,657],[573,1577,1579,1582],{"className":1578},[656],[573,1580,602],{"className":1581},[656,657],[573,1583,1585],{"className":1584},[701],[573,1586,1588],{"className":1587},[705],[573,1589,1591],{"className":1590},[709],[573,1592,1594],{"className":1593,"style":714},[713],[573,1595,1596,1599],{"style":717},[573,1597],{"className":1598,"style":722},[721],[573,1600,1602],{"className":1601},[726,727,728,729],[573,1603,620],{"className":1604},[656,729],[573,1606],{"className":1607,"style":736},[673],[573,1609,623],{"className":1610},[740],[573,1612],{"className":1613,"style":736},[673],[573,1615,1617,1621,1624],{"className":1616},[647],[573,1618],{"className":1619,"style":1620},[651],"height:0.6944em;",[573,1622,626],{"className":1623},[656,657],[573,1625,602],{"className":1626},[656,657]," ist dieselbe wie ",[573,1629,1631,1644],{"className":1630},[576],[573,1632,1634],{"className":1633},[580],[582,1635,1636],{"xmlns":584},[586,1637,1638,1642],{},[589,1639,1640],{},[592,1641,594],{},[635,1643,594],{"encoding":637},[573,1645,1647],{"className":1646,"ariaHidden":643},[642],[573,1648,1650,1653],{"className":1649},[647],[573,1651],{"className":1652,"style":1008},[651],[573,1654,594],{"className":1655,"style":658},[656,657],", nur um ",[573,1658,1660,1673],{"className":1659},[576],[573,1661,1663],{"className":1662},[580],[582,1664,1665],{"xmlns":584},[586,1666,1667,1671],{},[589,1668,1669],{},[592,1670,633],{},[635,1672,633],{"encoding":637},[573,1674,1676],{"className":1675,"ariaHidden":643},[642],[573,1677,1679,1682],{"className":1678},[647],[573,1680],{"className":1681,"style":772},[651],[573,1683,633],{"className":1684},[656,657]," nach unten verschoben, hat also denselben ",[573,1687,1689,1707],{"className":1688},[576],[573,1690,1692],{"className":1691},[580],[582,1693,1694],{"xmlns":584},[586,1695,1696,1704],{},[589,1697,1698],{},[797,1699,1700,1702],{},[592,1701,602],{},[592,1703,803],{},[635,1705,1706],{"encoding":637},"x_S",[573,1708,1710],{"className":1709,"ariaHidden":643},[642],[573,1711,1713,1716],{"className":1712},[647],[573,1714],{"className":1715,"style":832},[651],[573,1717,1719,1722],{"className":1718},[656],[573,1720,602],{"className":1721},[656,657],[573,1723,1725],{"className":1724},[701],[573,1726,1728,1748],{"className":1727},[705,845],[573,1729,1731,1745],{"className":1730},[709],[573,1732,1734],{"className":1733,"style":852},[713],[573,1735,1736,1739],{"style":855},[573,1737],{"className":1738,"style":722},[721],[573,1740,1742],{"className":1741},[726,727,728,729],[573,1743,803],{"className":1744,"style":865},[656,657,729],[573,1746,870],{"className":1747},[869],[573,1749,1751],{"className":1750},[709],[573,1752,1754],{"className":1753,"style":877},[713],[573,1755],{},". Ihre Nullstellen findet man durch Ausklammern:",[573,1758,1761],{"className":1759},[1760],"katex-display",[573,1762,1764,1845],{"className":1763},[576],[573,1765,1767],{"className":1766},[580],[582,1768,1770],{"xmlns":584,"display":1769},"block",[586,1771,1772,1842],{},[589,1773,1774,1776,1782,1784,1786,1788,1790,1792,1794,1796,1798,1800,1802,1804,1806,1808,1812,1815,1817,1819,1821,1823,1825,1828,1830,1832,1834,1836],{},[592,1775,611],{},[613,1777,1778,1780],{},[592,1779,602],{},[618,1781,620],{},[596,1783,623],{},[592,1785,626],{},[592,1787,602],{},[596,1789,608],{},[592,1791,602],{},[596,1793,599],{"stretchy":598},[592,1795,611],{},[592,1797,602],{},[596,1799,623],{},[592,1801,626],{},[596,1803,605],{"stretchy":598},[596,1805,608],{},[618,1807,1187],{},[1809,1810,1811],"mtext",{},"  ",[596,1813,1814],{},"⇔",[1809,1816,1811],{},[592,1818,602],{},[596,1820,608],{},[618,1822,1187],{},[1809,1824,1811],{},[1809,1826,1827],{},"oder",[1809,1829,1811],{},[592,1831,602],{},[596,1833,608],{},[596,1835,808],{},[810,1837,1838,1840],{},[592,1839,626],{},[592,1841,611],{},[635,1843,1844],{"encoding":637},"ax^2 + bx = x(ax + b) = 0 \\;\\Leftrightarrow\\; x = 0 \\;\\text{oder}\\; x = -\\frac{b}{a}",[573,1846,1848,1898,1919,1946,1967,1991,2009,2043],{"className":1847,"ariaHidden":643},[642],[573,1849,1851,1855,1858,1889,1892,1895],{"className":1850},[647],[573,1852],{"className":1853,"style":1854},[651],"height:0.9474em;vertical-align:-0.0833em;",[573,1856,611],{"className":1857},[656,657],[573,1859,1861,1864],{"className":1860},[656],[573,1862,602],{"className":1863},[656,657],[573,1865,1867],{"className":1866},[701],[573,1868,1870],{"className":1869},[705],[573,1871,1873],{"className":1872},[709],[573,1874,1877],{"className":1875,"style":1876},[713],"height:0.8641em;",[573,1878,1880,1883],{"style":1879},"top:-3.113em;margin-right:0.05em;",[573,1881],{"className":1882,"style":722},[721],[573,1884,1886],{"className":1885},[726,727,728,729],[573,1887,620],{"className":1888},[656,729],[573,1890],{"className":1891,"style":736},[673],[573,1893,623],{"className":1894},[740],[573,1896],{"className":1897,"style":736},[673],[573,1899,1901,1904,1907,1910,1913,1916],{"className":1900},[647],[573,1902],{"className":1903,"style":1620},[651],[573,1905,626],{"className":1906},[656,657],[573,1908,602],{"className":1909},[656,657],[573,1911],{"className":1912,"style":674},[673],[573,1914,608],{"className":1915},[678],[573,1917],{"className":1918,"style":674},[673],[573,1920,1922,1925,1928,1931,1934,1937,1940,1943],{"className":1921},[647],[573,1923],{"className":1924,"style":652},[651],[573,1926,602],{"className":1927},[656,657],[573,1929,599],{"className":1930},[662],[573,1932,611],{"className":1933},[656,657],[573,1935,602],{"className":1936},[656,657],[573,1938],{"className":1939,"style":736},[673],[573,1941,623],{"className":1942},[740],[573,1944],{"className":1945,"style":736},[673],[573,1947,1949,1952,1955,1958,1961,1964],{"className":1948},[647],[573,1950],{"className":1951,"style":652},[651],[573,1953,626],{"className":1954},[656,657],[573,1956,605],{"className":1957},[669],[573,1959],{"className":1960,"style":674},[673],[573,1962,608],{"className":1963},[678],[573,1965],{"className":1966,"style":674},[673],[573,1968,1970,1973,1976,1979,1982,1985,1988],{"className":1969},[647],[573,1971],{"className":1972,"style":1219},[651],[573,1974,1187],{"className":1975},[656],[573,1977],{"className":1978,"style":674},[673],[573,1980],{"className":1981,"style":674},[673],[573,1983,1814],{"className":1984},[678],[573,1986],{"className":1987,"style":674},[673],[573,1989],{"className":1990,"style":674},[673],[573,1992,1994,1997,2000,2003,2006],{"className":1993},[647],[573,1995],{"className":1996,"style":772},[651],[573,1998,602],{"className":1999},[656,657],[573,2001],{"className":2002,"style":674},[673],[573,2004,608],{"className":2005},[678],[573,2007],{"className":2008,"style":674},[673],[573,2010,2012,2015,2018,2021,2028,2031,2034,2037,2040],{"className":2011},[647],[573,2013],{"className":2014,"style":1620},[651],[573,2016,1187],{"className":2017},[656],[573,2019],{"className":2020,"style":674},[673],[573,2022,2025],{"className":2023},[656,2024],"text",[573,2026,1827],{"className":2027},[656],[573,2029],{"className":2030,"style":674},[673],[573,2032,602],{"className":2033},[656,657],[573,2035],{"className":2036,"style":674},[673],[573,2038,608],{"className":2039},[678],[573,2041],{"className":2042,"style":674},[673],[573,2044,2046,2050,2053],{"className":2045},[647],[573,2047],{"className":2048,"style":2049},[651],"height:2.0574em;vertical-align:-0.686em;",[573,2051,808],{"className":2052},[656],[573,2054,2056,2059,2116],{"className":2055},[656],[573,2057],{"className":2058},[662,905],[573,2060,2062],{"className":2061},[810],[573,2063,2065,2107],{"className":2064},[705,845],[573,2066,2068,2104],{"className":2067},[709],[573,2069,2072,2084,2092],{"className":2070,"style":2071},[713],"height:1.3714em;",[573,2073,2075,2078],{"style":2074},"top:-2.314em;",[573,2076],{"className":2077,"style":925},[721],[573,2079,2081],{"className":2080},[656],[573,2082,611],{"className":2083},[656,657],[573,2085,2086,2089],{"style":940},[573,2087],{"className":2088,"style":925},[721],[573,2090],{"className":2091,"style":948},[947],[573,2093,2095,2098],{"style":2094},"top:-3.677em;",[573,2096],{"className":2097,"style":925},[721],[573,2099,2101],{"className":2100},[656],[573,2102,626],{"className":2103},[656,657],[573,2105,870],{"className":2106},[869],[573,2108,2110],{"className":2109},[709],[573,2111,2114],{"className":2112,"style":2113},[713],"height:0.686em;",[573,2115],{},[573,2117],{"className":2118},[669,905],[564,2120,2121,2122,979],{},"Die Mitte dazwischen ist 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= 2x^2 - 8x + 5",[573,2346,2348,2375,2422,2444],{"className":2347,"ariaHidden":643},[642],[573,2349,2351,2354,2357,2360,2363,2366,2369,2372],{"className":2350},[647],[573,2352],{"className":2353,"style":652},[651],[573,2355,594],{"className":2356,"style":658},[656,657],[573,2358,599],{"className":2359},[662],[573,2361,602],{"className":2362},[656,657],[573,2364,605],{"className":2365},[669],[573,2367],{"className":2368,"style":674},[673],[573,2370,608],{"className":2371},[678],[573,2373],{"className":2374,"style":674},[673],[573,2376,2378,2381,2384,2413,2416,2419],{"className":2377},[647],[573,2379],{"className":2380,"style":688},[651],[573,2382,620],{"className":2383},[656],[573,2385,2387,2390],{"className":2386},[656],[573,2388,602],{"className":2389},[656,657],[573,2391,2393],{"className":2392},[701],[573,2394,2396],{"className":2395},[705],[573,2397,2399],{"className":2398},[709],[573,2400,2402],{"className":2401,"style":714},[713],[573,2403,2404,2407],{"style":717},[573,2405],{"className":2406,"style":722},[721],[573,2408,2410],{"className":2409},[726,727,728,729],[573,2411,620],{"className":2412},[656,729],[573,2414],{"className":2415,"style":736},[673],[573,2417,808],{"className":2418},[740],[573,2420],{"className":2421,"style":736},[673],[573,2423,2425,2429,2432,2435,2438,2441],{"className":2424},[647],[573,2426],{"className":2427,"style":2428},[651],"height:0.7278em;vertical-align:-0.0833em;",[573,2430,2334],{"className":2431},[656],[573,2433,602],{"className":2434},[656,657],[573,2436],{"className":2437,"style":736},[673],[573,2439,623],{"className":2440},[740],[573,2442],{"className":2443,"style":736},[673],[573,2445,2447,2450],{"className":2446},[647],[573,2448],{"className":2449,"style":1219},[651],[573,2451,2341],{"className":2452},[656],", also ",[573,2455,2457,2475],{"className":2456},[576],[573,2458,2460],{"className":2459},[580],[582,2461,2462],{"xmlns":584},[586,2463,2464,2472],{},[589,2465,2466,2468,2470],{},[592,2467,611],{},[596,2469,608],{},[618,2471,620],{},[635,2473,2474],{"encoding":637},"a = 2",[573,2476,2478,2496],{"className":2477,"ariaHidden":643},[642],[573,2479,2481,2484,2487,2490,2493],{"className":2480},[647],[573,2482],{"className":2483,"style":772},[651],[573,2485,611],{"className":2486},[656,657],[573,2488],{"className":2489,"style":674},[673],[573,2491,608],{"className":2492},[678],[573,2494],{"className":2495,"style":674},[673],[573,2497,2499,2502],{"className":2498},[647],[573,2500],{"className":2501,"style":1219},[651],[573,2503,620],{"className":2504},[656]," und ",[573,2507,2509,2529],{"className":2508},[576],[573,2510,2512],{"className":2511},[580],[582,2513,2514],{"xmlns":584},[586,2515,2516,2526],{},[589,2517,2518,2520,2522,2524],{},[592,2519,626],{},[596,2521,608],{},[596,2523,808],{},[618,2525,2334],{},[635,2527,2528],{"encoding":637},"b = -8",[573,2530,2532,2550],{"className":2531,"ariaHidden":643},[642],[573,2533,2535,2538,2541,2544,2547],{"className":2534},[647],[573,2536],{"className":2537,"style":1620},[651],[573,2539,626],{"className":2540},[656,657],[573,2542],{"className":2543,"style":674},[673],[573,2545,608],{"className":2546},[678],[573,2548],{"className":2549,"style":674},[673],[573,2551,2553,2556,2559],{"className":2552},[647],[573,2554],{"className":2555,"style":2428},[651],[573,2557,808],{"className":2558},[656],[573,2560,2334],{"className":2561},[656],":",[573,2564,2566],{"className":2565},[1760],[573,2567,2569,2658],{"className":2568},[576],[573,2570,2572],{"className":2571},[580],[582,2573,2574],{"xmlns":584,"display":1769},[586,2575,2576,2655],{},[589,2577,2578,2584,2586,2588,2605,2607,2609,2612,2615,2621,2623,2625,2627,2629,2631,2633,2635,2637,2639,2641,2644,2646,2648,2650,2652],{},[797,2579,2580,2582],{},[592,2581,602],{},[592,2583,803],{},[596,2585,608],{},[596,2587,808],{},[810,2589,2590,2596],{},[589,2591,2592,2594],{},[596,2593,808],{},[618,2595,2334],{},[589,2597,2598,2600,2603],{},[618,2599,620],{},[596,2601,2602],{},"⋅",[618,2604,620],{},[596,2606,608],{},[618,2608,620],{},[596,2610,2611],{"separator":643},",",[673,2613],{"width":2614},"2em",[797,2616,2617,2619],{},[592,2618,1029],{},[592,2620,803],{},[596,2622,608],{},[592,2624,594],{},[596,2626,599],{"stretchy":598},[618,2628,620],{},[596,2630,605],{"stretchy":598},[596,2632,608],{},[618,2634,620],{},[596,2636,2602],{},[618,2638,1313],{},[596,2640,808],{},[618,2642,2643],{},"16",[596,2645,623],{},[618,2647,2341],{},[596,2649,608],{},[596,2651,808],{},[618,2653,2654],{},"3",[635,2656,2657],{"encoding":637},"x_S = -\\frac{-8}{2 \\cdot 2} = 2, \\qquad y_S = f(2) = 2 \\cdot 4 - 16 + 5 = -3",[573,2659,2661,2716,2813,2884,2911,2929,2947,2965,2983],{"className":2660,"ariaHidden":643},[642],[573,2662,2664,2667,2707,2710,2713],{"className":2663},[647],[573,2665],{"className":2666,"style":832},[651],[573,2668,2670,2673],{"className":2669},[656],[573,2671,602],{"className":2672},[656,657],[573,2674,2676],{"className":2675},[701],[573,2677,2679,2699],{"className":2678},[705,845],[573,2680,2682,2696],{"className":2681},[709],[573,2683,2685],{"className":2684,"style":852},[713],[573,2686,2687,2690],{"style":855},[573,2688],{"className":2689,"style":722},[721],[573,2691,2693],{"className":2692},[726,727,728,729],[573,2694,803],{"className":2695,"style":865},[656,657,729],[573,2697,870],{"className":2698},[869],[573,2700,2702],{"className":2701},[709],[573,2703,2705],{"className":2704,"style":877},[713],[573,2706],{},[573,2708],{"className":2709,"style":674},[673],[573,2711,608],{"className":2712},[678],[573,2714],{"className":2715,"style":674},[673],[573,2717,2719,2723,2726,2804,2807,2810],{"className":2718},[647],[573,2720],{"className":2721,"style":2722},[651],"height:2.0074em;vertical-align:-0.686em;",[573,2724,808],{"className":2725},[656],[573,2727,2729,2732,2801],{"className":2728},[656],[573,2730],{"className":2731},[662,905],[573,2733,2735],{"className":2734},[810],[573,2736,2738,2793],{"className":2737},[705,845],[573,2739,2741,2790],{"className":2740},[709],[573,2742,2745,2768,2776],{"className":2743,"style":2744},[713],"height:1.3214em;",[573,2746,2747,2750],{"style":2074},[573,2748],{"className":2749,"style":925},[721],[573,2751,2753,2756,2759,2762,2765],{"className":2752},[656],[573,2754,620],{"className":2755},[656],[573,2757],{"className":2758,"style":736},[673],[573,2760,2602],{"className":2761},[740],[573,2763],{"className":2764,"style":736},[673],[573,2766,620],{"className":2767},[656],[573,2769,2770,2773],{"style":940},[573,2771],{"className":2772,"style":925},[721],[573,2774],{"className":2775,"style":948},[947],[573,2777,2778,2781],{"style":2094},[573,2779],{"className":2780,"style":925},[721],[573,2782,2784,2787],{"className":2783},[656],[573,2785,808],{"className":2786},[656],[573,2788,2334],{"className":2789},[656],[573,2791,870],{"className":2792},[869],[573,2794,2796],{"className":2795},[709],[573,2797,2799],{"className":2798,"style":2113},[713],[573,2800],{},[573,2802],{"className":2803},[669,905],[573,2805],{"className":2806,"style":674},[673],[573,2808,608],{"className":2809},[678],[573,2811],{"className":2812,"style":674},[673],[573,2814,2816,2820,2823,2827,2831,2835,2875,2878,2881],{"className":2815},[647],[573,2817],{"className":2818,"style":2819},[651],"height:0.8389em;vertical-align:-0.1944em;",[573,2821,620],{"className":2822},[656],[573,2824,2611],{"className":2825},[2826],"mpunct",[573,2828],{"className":2829,"style":2830},[673],"margin-right:2em;",[573,2832],{"className":2833,"style":2834},[673],"margin-right:0.1667em;",[573,2836,2838,2841],{"className":2837},[656],[573,2839,1029],{"className":2840,"style":1065},[656,657],[573,2842,2844],{"className":2843},[701],[573,2845,2847,2867],{"className":2846},[705,845],[573,2848,2850,2864],{"className":2849},[709],[573,2851,2853],{"className":2852,"style":852},[713],[573,2854,2855,2858],{"style":1080},[573,2856],{"className":2857,"style":722},[721],[573,2859,2861],{"className":2860},[726,727,728,729],[573,2862,803],{"className":2863,"style":865},[656,657,729],[573,2865,870],{"className":2866},[869],[573,2868,2870],{"className":2869},[709],[573,2871,2873],{"className":2872,"style":877},[713],[573,2874],{},[573,2876],{"className":2877,"style":674},[673],[573,2879,608],{"className":2880},[678],[573,2882],{"className":2883,"style":674},[673],[573,2885,2887,2890,2893,2896,2899,2902,2905,2908],{"className":2886},[647],[573,2888],{"className":2889,"style":652},[651],[573,2891,594],{"className":2892,"style":658},[656,657],[573,2894,599],{"className":2895},[662],[573,2897,620],{"className":2898},[656],[573,2900,605],{"className":2901},[669],[573,2903],{"className":2904,"style":674},[673],[573,2906,608],{"className":2907},[678],[573,2909],{"className":2910,"style":674},[673],[573,2912,2914,2917,2920,2923,2926],{"className":2913},[647],[573,2915],{"className":2916,"style":1219},[651],[573,2918,620],{"className":2919},[656],[573,2921],{"className":2922,"style":736},[673],[573,2924,2602],{"className":2925},[740],[573,2927],{"className":2928,"style":736},[673],[573,2930,2932,2935,2938,2941,2944],{"className":2931},[647],[573,2933],{"className":2934,"style":2428},[651],[573,2936,1313],{"className":2937},[656],[573,2939],{"className":2940,"style":736},[673],[573,2942,808],{"className":2943},[740],[573,2945],{"className":2946,"style":736},[673],[573,2948,2950,2953,2956,2959,2962],{"className":2949},[647],[573,2951],{"className":2952,"style":2428},[651],[573,2954,2643],{"className":2955},[656],[573,2957],{"className":2958,"style":736},[673],[573,2960,623],{"className":2961},[740],[573,2963],{"className":2964,"style":736},[673],[573,2966,2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Scheitelpunkt ist ",[573,2999,3001,3028],{"className":3000},[576],[573,3002,3004],{"className":3003},[580],[582,3005,3006],{"xmlns":584},[586,3007,3008,3025],{},[589,3009,3010,3012,3014,3016,3019,3021,3023],{},[592,3011,803],{},[596,3013,599],{"stretchy":598},[618,3015,620],{},[596,3017,3018],{},"∣",[596,3020,808],{},[618,3022,2654],{},[596,3024,605],{"stretchy":598},[635,3026,3027],{"encoding":637},"S(2 \\mid 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= -\\frac{3}{2 \\cdot (-0{,}5)} = 3, \\qquad y_S = f(3) = -4{,}5 + 9 + 1 = 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\\mid 5{,}5)",[573,3875,3877,3901],{"className":3876,"ariaHidden":643},[642],[573,3878,3880,3883,3886,3889,3892,3895,3898],{"className":3879},[647],[573,3881],{"className":3882,"style":652},[651],[573,3884,803],{"className":3885,"style":865},[656,657],[573,3887,599],{"className":3888},[662],[573,3890,2654],{"className":3891},[656],[573,3893],{"className":3894,"style":674},[673],[573,3896,3018],{"className":3897},[678],[573,3899],{"className":3900,"style":674},[673],[573,3902,3904,3907,3910,3916,3919],{"className":3903},[647],[573,3905],{"className":3906,"style":652},[651],[573,3908,2341],{"className":3909},[656],[573,3911,3913],{"className":3912},[656],[573,3914,2611],{"className":3915},[2826],[573,3917,2341],{"className":3918},[656],[573,3920,605],{"className":3921},[669],", ein Hochpunkt, weil 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",[573,3984,3986,3999],{"className":3985},[576],[573,3987,3989],{"className":3988},[580],[582,3990,3991],{"xmlns":584},[586,3992,3993,3997],{},[589,3994,3995],{},[592,3996,626],{},[635,3998,626],{"encoding":637},[573,4000,4002],{"className":4001,"ariaHidden":643},[642],[573,4003,4005,4008],{"className":4004},[647],[573,4006],{"className":4007,"style":1620},[651],[573,4009,626],{"className":4010},[656,657],": ",[573,4013,4015,4045],{"className":4014},[576],[573,4016,4018],{"className":4017},[580],[582,4019,4020],{"xmlns":584},[586,4021,4022,4042],{},[589,4023,4024,4026,4036,4038,4040],{},[596,4025,808],{},[810,4027,4028,4034],{},[589,4029,4030,4032],{},[596,4031,808],{},[618,4033,2334],{},[618,4035,1313],{},[596,4037,608],{},[596,4039,623],{},[618,4041,620],{},[635,4043,4044],{"encoding":637},"-\\frac{-8}{4} = +2",[573,4046,4048,4139],{"className":4047,"ariaHidden":643},[642],[573,4049,4051,4055,4058,4130,4133,4136],{"className":4050},[647],[573,4052],{"className":4053,"style":4054},[651],"height:1.1901em;vertical-align:-0.345em;",[573,4056,808],{"className":4057},[656],[573,4059,4061,4064,4127],{"className":4060},[656],[573,4062],{"className":4063},[662,905],[573,4065,4067],{"className":4066},[810],[573,4068,4070,4119],{"className":4069},[705,845],[573,4071,4073,4116],{"className":4072},[709],[573,4074,4077,4091,4099],{"className":4075,"style":4076},[713],"height:0.8451em;",[573,4078,4079,4082],{"style":921},[573,4080],{"className":4081,"style":925},[721],[573,4083,4085],{"className":4084},[726,727,728,729],[573,4086,4088],{"className":4087},[656,729],[573,4089,1313],{"className":4090},[656,729],[573,4092,4093,4096],{"style":940},[573,4094],{"className":4095,"style":925},[721],[573,4097],{"className":4098,"style":948},[947],[573,4100,4101,4104],{"style":951},[573,4102],{"className":4103,"style":925},[721],[573,4105,4107],{"className":4106},[726,727,728,729],[573,4108,4110,4113],{"className":4109},[656,729],[573,4111,808],{"className":4112},[656,729],[573,4114,2334],{"className":4115},[656,729],[573,4117,870],{"className":4118},[869],[573,4120,4122],{"className":4121},[709],[573,4123,4125],{"className":4124,"style":973},[713],[573,4126],{},[573,4128],{"className":4129},[669,905],[573,4131],{"className":4132,"style":674},[673],[573,4134,608],{"className":4135},[678],[573,4137],{"className":4138,"style":674},[673],[573,4140,4142,4145,4148],{"className":4141},[647],[573,4143],{"className":4144,"style":2428},[651],[573,4146,623],{"className":4147},[656],[573,4149,620],{"className":4150},[656],[781,4152,4153,4154,4182,4183,4211,4212,4246,4247,4357,4358,979],{},"Nur durch ",[573,4155,4157,4170],{"className":4156},[576],[573,4158,4160],{"className":4159},[580],[582,4161,4162],{"xmlns":584},[586,4163,4164,4168],{},[589,4165,4166],{},[618,4167,620],{},[635,4169,620],{"encoding":637},[573,4171,4173],{"className":4172,"ariaHidden":643},[642],[573,4174,4176,4179],{"className":4175},[647],[573,4177],{"className":4178,"style":1219},[651],[573,4180,620],{"className":4181},[656]," teilen und dann mit ",[573,4184,4186,4199],{"className":4185},[576],[573,4187,4189],{"className":4188},[580],[582,4190,4191],{"xmlns":584},[586,4192,4193,4197],{},[589,4194,4195],{},[592,4196,611],{},[635,4198,611],{"encoding":637},[573,4200,4202],{"className":4201,"ariaHidden":643},[642],[573,4203,4205,4208],{"className":4204},[647],[573,4206],{"className":4207,"style":772},[651],[573,4209,611],{"className":4210},[656,657]," multiplizieren: Der Nenner ist ",[573,4213,4215,4231],{"className":4214},[576],[573,4216,4218],{"className":4217},[580],[582,4219,4220],{"xmlns":584},[586,4221,4222,4228],{},[589,4223,4224,4226],{},[618,4225,620],{},[592,4227,611],{},[635,4229,4230],{"encoding":637},"2a",[573,4232,4234],{"className":4233,"ariaHidden":643},[642],[573,4235,4237,4240,4243],{"className":4236},[647],[573,4238],{"className":4239,"style":1219},[651],[573,4241,620],{"className":4242},[656],[573,4244,611],{"className":4245},[656,657]," als Ganzes, also ",[573,4248,4250,4274],{"className":4249},[576],[573,4251,4253],{"className":4252},[580],[582,4254,4255],{"xmlns":584},[586,4256,4257,4271],{},[589,4258,4259,4261],{},[596,4260,808],{},[810,4262,4263,4265],{},[592,4264,626],{},[589,4266,4267,4269],{},[618,4268,620],{},[592,4270,611],{},[635,4272,4273],{"encoding":637},"-\\frac{b}{2a}",[573,4275,4277],{"className":4276,"ariaHidden":643},[642],[573,4278,4280,4283,4286],{"className":4279},[647],[573,4281],{"className":4282,"style":895},[651],[573,4284,808],{"className":4285},[656],[573,4287,4289,4292,4354],{"className":4288},[656],[573,4290],{"className":4291},[662,905],[573,4293,4295],{"className":4294},[810],[573,4296,4298,4346],{"className":4297},[705,845],[573,4299,4301,4343],{"className":4300},[709],[573,4302,4304,4321,4329],{"className":4303,"style":918},[713],[573,4305,4306,4309],{"style":921},[573,4307],{"className":4308,"style":925},[721],[573,4310,4312],{"className":4311},[726,727,728,729],[573,4313,4315,4318],{"className":4314},[656,729],[573,4316,620],{"className":4317},[656,729],[573,4319,611],{"className":4320},[656,657,729],[573,4322,4323,4326],{"style":940},[573,4324],{"className":4325,"style":925},[721],[573,4327],{"className":4328,"style":948},[947],[573,4330,4331,4334],{"style":951},[573,4332],{"className":4333,"style":925},[721],[573,4335,4337],{"className":4336},[726,727,728,729],[573,4338,4340],{"className":4339},[656,729],[573,4341,626],{"className":4342},[656,657,729],[573,4344,870],{"className":4345},[869],[573,4347,4349],{"className":4348},[709],[573,4350,4352],{"className":4351,"style":973},[713],[573,4353],{},[573,4355],{"className":4356},[669,905],", nicht ",[573,4359,4361,4385],{"className":4360},[576],[573,4362,4364],{"className":4363},[580],[582,4365,4366],{"xmlns":584},[586,4367,4368,4382],{},[589,4369,4370,4372,4378,4380],{},[596,4371,808],{},[810,4373,4374,4376],{},[592,4375,626],{},[618,4377,620],{},[596,4379,2602],{},[592,4381,611],{},[635,4383,4384],{"encoding":637},"-\\frac{b}{2} \\cdot a",[573,4386,4388,4474],{"className":4387,"ariaHidden":643},[642],[573,4389,4391,4394,4397,4465,4468,4471],{"className":4390},[647],[573,4392],{"className":4393,"style":895},[651],[573,4395,808],{"className":4396},[656],[573,4398,4400,4403,4462],{"className":4399},[656],[573,4401],{"className":4402},[662,905],[573,4404,4406],{"className":4405},[810],[573,4407,4409,4454],{"className":4408},[705,845],[573,4410,4412,4451],{"className":4411},[709],[573,4413,4415,4429,4437],{"className":4414,"style":918},[713],[573,4416,4417,4420],{"style":921},[573,4418],{"className":4419,"style":925},[721],[573,4421,4423],{"className":4422},[726,727,728,729],[573,4424,4426],{"className":4425},[656,729],[573,4427,620],{"className":4428},[656,729],[573,4430,4431,4434],{"style":940},[573,4432],{"className":4433,"style":925},[721],[573,4435],{"className":4436,"style":948},[947],[573,4438,4439,4442],{"style":951},[573,4440],{"className":4441,"style":925},[721],[573,4443,4445],{"className":4444},[726,727,728,729],[573,4446,4448],{"className":4447},[656,729],[573,4449,626],{"className":4450},[656,657,729],[573,4452,870],{"className":4453},[869],[573,4455,4457],{"className":4456},[709],[573,4458,4460],{"className":4459,"style":973},[713],[573,4461],{},[573,4463],{"className":4464},[669,905],[573,4466],{"className":4467,"style":736},[673],[573,4469,2602],{"className":4470},[740],[573,4472],{"className":4473,"style":736},[673],[573,4475,4477,4480],{"className":4476},[647],[573,4478],{"className":4479,"style":772},[651],[573,4481,611],{"className":4482},[656,657],[781,4484,4485,4555,4556,4625,4626,4675,4676,979],{},[573,4486,4488,4506],{"className":4487},[576],[573,4489,4491],{"className":4490},[580],[582,4492,4493],{"xmlns":584},[586,4494,4495,4503],{},[589,4496,4497],{},[797,4498,4499,4501],{},[592,4500,1029],{},[592,4502,803],{},[635,4504,4505],{"encoding":637},"y_S",[573,4507,4509],{"className":4508,"ariaHidden":643},[642],[573,4510,4512,4515],{"className":4511},[647],[573,4513],{"className":4514,"style":1058},[651],[573,4516,4518,4521],{"className":4517},[656],[573,4519,1029],{"className":4520,"style":1065},[656,657],[573,4522,4524],{"className":4523},[701],[573,4525,4527,4547],{"className":4526},[705,845],[573,4528,4530,4544],{"className":4529},[709],[573,4531,4533],{"className":4532,"style":852},[713],[573,4534,4535,4538],{"style":1080},[573,4536],{"className":4537,"style":722},[721],[573,4539,4541],{"className":4540},[726,727,728,729],[573,4542,803],{"className":4543,"style":865},[656,657,729],[573,4545,870],{"className":4546},[869],[573,4548,4550],{"className":4549},[709],[573,4551,4553],{"className":4552,"style":877},[713],[573,4554],{}," falsch ausrechnen, weil das Quadrat bei negativem ",[573,4557,4559,4576],{"className":4558},[576],[573,4560,4562],{"className":4561},[580],[582,4563,4564],{"xmlns":584},[586,4565,4566,4574],{},[589,4567,4568],{},[797,4569,4570,4572],{},[592,4571,602],{},[592,4573,803],{},[635,4575,1706],{"encoding":637},[573,4577,4579],{"className":4578,"ariaHidden":643},[642],[573,4580,4582,4585],{"className":4581},[647],[573,4583],{"className":4584,"style":832},[651],[573,4586,4588,4591],{"className":4587},[656],[573,4589,602],{"className":4590},[656,657],[573,4592,4594],{"className":4593},[701],[573,4595,4597,4617],{"className":4596},[705,845],[573,4598,4600,4614],{"className":4599},[709],[573,4601,4603],{"className":4602,"style":852},[713],[573,4604,4605,4608],{"style":855},[573,4606],{"className":4607,"style":722},[721],[573,4609,4611],{"className":4610},[726,727,728,729],[573,4612,803],{"className":4613,"style":865},[656,657,729],[573,4615,870],{"className":4616},[869],[573,4618,4620],{"className":4619},[709],[573,4621,4623],{"className":4622,"style":877},[713],[573,4624],{}," das Vorzeichen verliert: ",[573,4627,4629,4651],{"className":4628},[576],[573,4630,4632],{"className":4631},[580],[582,4633,4634],{"xmlns":584},[586,4635,4636,4648],{},[589,4637,4638,4640,4642,4644,4646],{},[592,4639,594],{},[596,4641,599],{"stretchy":598},[596,4643,808],{},[618,4645,620],{},[596,4647,605],{"stretchy":598},[635,4649,4650],{"encoding":637},"f(-2)",[573,4652,4654],{"className":4653,"ariaHidden":643},[642],[573,4655,4657,4660,4663,4666,4669,4672],{"className":4656},[647],[573,4658],{"className":4659,"style":652},[651],[573,4661,594],{"className":4662,"style":658},[656,657],[573,4664,599],{"className":4665},[662],[573,4667,808],{"className":4668},[656],[573,4670,620],{"className":4671},[656],[573,4673,605],{"className":4674},[669]," enthält ",[573,4677,4679,4713],{"className":4678},[576],[573,4680,4682],{"className":4681},[580],[582,4683,4684],{"xmlns":584},[586,4685,4686,4710],{},[589,4687,4688,4690,4692,4694,4696,4698,4704,4706,4708],{},[592,4689,611],{},[596,4691,2602],{},[596,4693,599],{"stretchy":598},[596,4695,808],{},[618,4697,620],{},[613,4699,4700,4702],{},[596,4701,605],{"stretchy":598},[618,4703,620],{},[596,4705,608],{},[618,4707,1313],{},[592,4709,611],{},[635,4711,4712],{"encoding":637},"a \\cdot (-2)^2 = 4a",[573,4714,4716,4735,4789],{"className":4715,"ariaHidden":643},[642],[573,4717,4719,4723,4726,4729,4732],{"className":4718},[647],[573,4720],{"className":4721,"style":4722},[651],"height:0.4445em;",[573,4724,611],{"className":4725},[656,657],[573,4727],{"className":4728,"style":736},[673],[573,4730,2602],{"className":4731},[740],[573,4733],{"className":4734,"style":736},[673],[573,4736,4738,4742,4745,4748,4751,4780,4783,4786],{"className":4737},[647],[573,4739],{"className":4740,"style":4741},[651],"height:1.0641em;vertical-align:-0.25em;",[573,4743,599],{"className":4744},[662],[573,4746,808],{"className":4747},[656],[573,4749,620],{"className":4750},[656],[573,4752,4754,4757],{"className":4753},[669],[573,4755,605],{"className":4756},[669],[573,4758,4760],{"className":4759},[701],[573,4761,4763],{"className":4762},[705],[573,4764,4766],{"className":4765},[709],[573,4767,4769],{"className":4768,"style":714},[713],[573,4770,4771,4774],{"style":717},[573,4772],{"className":4773,"style":722},[721],[573,4775,4777],{"className":4776},[726,727,728,729],[573,4778,620],{"className":4779},[656,729],[573,4781],{"className":4782,"style":674},[673],[573,4784,608],{"className":4785},[678],[573,4787],{"className":4788,"style":674},[673],[573,4790,4792,4795,4798],{"className":4791},[647],[573,4793],{"className":4794,"style":1219},[651],[573,4796,1313],{"className":4797},[656],[573,4799,611],{"className":4800},[656,657],{"title":4802,"searchDepth":4803,"depth":4803,"links":4804},"",2,[4805,4806,4807,4808],{"id":561,"depth":4803,"text":562},{"id":1508,"depth":4803,"text":1509},{"id":2296,"depth":4803,"text":2297},{"id":3975,"depth":4803,"text":3976},[4810,4813,4816,4819,4822,4825,4829],{"lhs":4811,"rhs":4812},"a*(-b\u002F(2*a))^2 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style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" 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role=\"img\" aria-label=\"Graph von f(x) = 2x² − 8x + 5; der Scheitelpunkt S(2 | −3) liegt mittig zwischen den Stellen 0 und 4 mit gleichem Funktionswert 5\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-vertex-from-general-form-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-vertex-from-general-form-clip\">\u003Crect x=\"0\" y=\"0\" width=\"276\" height=\"256.8\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cline x1=\"0\" y1=\"156\" x2=\"276\" y2=\"156\" class=\"fig-axis\" marker-end=\"url(#fig-vertex-from-general-form-arrow)\"\u002F>\u003Cline x1=\"46\" y1=\"256.8\" x2=\"46\" y2=\"0\" class=\"fig-axis\" marker-end=\"url(#fig-vertex-from-general-form-arrow)\"\u002F>\u003Cline x1=\"0\" y1=\"153\" x2=\"0\" y2=\"159\" class=\"fig-axis\"\u002F>\u003Ctext x=\"3\" y=\"170\" 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212.13 L 165.6 210.72 L 166.75 209.25 L 167.9 207.72 L 169.05 206.13 L 170.2 204.48 L 171.35 202.77 L 172.5 201 L 173.65 199.17 L 174.8 197.28 L 175.95 195.33 L 177.1 193.32 L 178.25 191.25 L 179.4 189.12 L 180.55 186.93 L 181.7 184.68 L 182.85 182.37 L 184 180 L 185.15 177.57 L 186.3 175.08 L 187.45 172.53 L 188.6 169.92 L 189.75 167.25 L 190.9 164.52 L 192.05 161.73 L 193.2 158.88 L 194.35 155.97 L 195.5 153 L 196.65 149.97 L 197.8 146.88 L 198.95 143.73 L 200.1 140.52 L 201.25 137.25 L 202.4 133.92 L 203.55 130.53 L 204.7 127.08 L 205.85 123.57 L 207 120 L 208.15 116.37 L 209.3 112.68 L 210.45 108.93 L 211.6 105.12 L 212.75 101.25 L 213.9 97.32 L 215.05 93.33 L 216.2 89.28 L 217.35 85.17 L 218.5 81 L 219.65 76.77 L 220.8 72.48 L 221.95 68.13 L 223.1 63.72 L 224.25 59.25 L 225.4 54.72 L 226.55 50.13 L 227.7 45.48 L 228.85 40.77 L 230 36 L 231.15 31.17 L 232.3 26.28 L 233.45 21.33 L 234.6 16.32 L 235.75 11.25 L 236.9 6.12 L 238.05 0.93 L 239.2 -4.32 L 240.35 -9.63 L 241.5 -15 L 242.65 -20.43 L 243.8 -25.92 L 244.95 -31.47 L 246.1 -37.08 L 247.25 -42.75 L 248.4 -48.48 L 249.55 -54.27 L 250.7 -60.12 L 251.85 -66.03 L 253 -72 L 254.15 -78.03 L 255.3 -84.12 L 256.45 -90.27 L 257.6 -96.48 L 258.75 -102.75 L 259.9 -109.08 L 261.05 -115.47 L 262.2 -121.92 L 263.35 -128.43 L 264.5 -135 L 265.65 -141.63 L 266.8 -148.32 L 267.95 -155.07 L 269.1 -161.88 L 270.25 -168.75 L 271.4 -175.68 L 272.55 -182.67 L 273.7 -189.72 L 274.85 -196.83 L 276 -204\" class=\"fig-main fig-graph\" clip-path=\"url(#fig-vertex-from-general-form-clip)\"\u002F>\u003Ccircle cx=\"46\" cy=\"36\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"230\" cy=\"36\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"138\" cy=\"228\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"146\" y=\"236\" text-anchor=\"start\" dominant-baseline=\"middle\" class=\"fig-label fig-upright\">S(2 | −3)\u003C\u002Ftext>\u003C\u002Fsvg>","vertex-from-general-form","x_S = -\\frac{b}{2a}, \\quad y_S = f(x_S)","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>S\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>b\u003C\u002Fmi>\u003Cmrow>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"1em\"\u002F>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmi>S\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>S\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_S = -\\frac{b}{2a}, \\quad y_S = 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xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":626,"meaning":4904,"symbolHtml":4905},"Koeffizient vor x in f(x) = ax² + bx + c","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":594,"meaning":4907,"symbolHtml":4908},"die quadratische Funktion f(x) = ax² + bx + c","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","mstpSHUnJW8-YTjjG8jnrzLGkUNeXIdowNfbP98Xyqg",[4911,4914,4917,4920],{"stem":4912,"title":4913,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fabc-formel","abc-Formel (Mitternachtsformel)",{"stem":4915,"title":4916,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fquadratische-ergaenzung","Quadratische Ergänzung",{"stem":4918,"title":4919,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fquadratische-funktion","Quadratische Funktion",{"stem":4921,"title":4922,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fscheitelpunktform","Scheitelpunktform",1793824275057]