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c",[576,1199,1201,1231],{"className":1200,"ariaHidden":614},[613],[576,1202,1204,1207,1211,1215,1218,1222,1225,1228],{"className":1203},[618],[576,1205],{"className":1206,"style":984},[622],[576,1208,1180],{"className":1209,"style":1210},[627,631],"margin-right:0.1076em;",[576,1212,1184],{"className":1213},[1214],"mopen",[576,1216,689],{"className":1217},[627],[576,1219,1189],{"className":1220},[1221],"mclose",[576,1223],{"className":1224,"style":710},[709],[576,1226,755],{"className":1227},[714],[576,1229],{"className":1230,"style":710},[709],[576,1232,1234,1237],{"className":1233},[618],[576,1235],{"className":1236,"style":800},[622],[576,1238,1194],{"className":1239},[627,631],", die Parabel schneidet die y-Achse in ",[576,1242,1244,1266],{"className":1243},[579],[576,1245,1247],{"className":1246},[583],[585,1248,1249],{"xmlns":587},[589,1250,1251,1263],{},[592,1252,1253,1255,1257,1259,1261],{},[683,1254,1184],{"stretchy":1183},[602,1256,689],{},[683,1258,962],{},[598,1260,1194],{},[683,1262,1189],{"stretchy":1183},[606,1264,1265],{"encoding":608},"(0 \\mid c)",[576,1267,1269,1290],{"className":1268,"ariaHidden":614},[613],[576,1270,1272,1275,1278,1281,1284,1287],{"className":1271},[618],[576,1273],{"className":1274,"style":984},[622],[576,1276,1184],{"className":1277},[1214],[576,1279,689],{"className":1280},[627],[576,1282],{"className":1283,"style":710},[709],[576,1285,962],{"className":1286},[714],[576,1288],{"className":1289,"style":710},[709],[576,1291,1293,1296,1299],{"className":1292},[618],[576,1294],{"className":1295,"style":984},[622],[576,1297,1194],{"className":1298},[627,631],[576,1300,1189],{"className":1301},[1221],".",[564,1304,1305,1306,1309,1310,1506,1507,1510,1511,1577,1578,1606],{},"Der tiefste bzw. höchste Punkt heißt ",[568,1307,1308],{},"Scheitelpunkt",". Seine x-Koordinate ist ",[576,1311,1313,1350],{"className":1312},[579],[576,1314,1316],{"className":1315},[583],[585,1317,1318],{"xmlns":587},[589,1319,1320,1347],{},[592,1321,1322,1330,1332,1335],{},[1323,1324,1325,1327],"msub",{},[598,1326,600],{},[598,1328,1329],{},"S",[683,1331,755],{},[683,1333,1334],{},"−",[1336,1337,1338,1341],"mfrac",{},[598,1339,1340],{},"b",[592,1342,1343,1345],{},[602,1344,604],{},[598,1346,681],{},[606,1348,1349],{"encoding":608},"x_S = -\\frac{b}{2a}",[576,1351,1353,1416],{"className":1352,"ariaHidden":614},[613],[576,1354,1356,1360,1407,1410,1413],{"className":1355},[618],[576,1357],{"className":1358,"style":1359},[622],"height:0.5806em;vertical-align:-0.15em;",[576,1361,1363,1366],{"className":1362},[627],[576,1364,600],{"className":1365},[627,631],[576,1367,1369],{"className":1368},[635],[576,1370,1373,1398],{"className":1371},[639,1372],"vlist-t2",[576,1374,1376,1393],{"className":1375},[643],[576,1377,1380],{"className":1378,"style":1379},[647],"height:0.3283em;",[576,1381,1383,1386],{"style":1382},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[576,1384],{"className":1385,"style":655},[654],[576,1387,1389],{"className":1388},[659,660,661,662],[576,1390,1329],{"className":1391,"style":1392},[627,631,662],"margin-right:0.0576em;",[576,1394,1397],{"className":1395},[1396],"vlist-s","​",[576,1399,1401],{"className":1400},[643],[576,1402,1405],{"className":1403,"style":1404},[647],"height:0.15em;",[576,1406],{},[576,1408],{"className":1409,"style":710},[709],[576,1411,755],{"className":1412},[714],[576,1414],{"className":1415,"style":710},[709],[576,1417,1419,1423,1426],{"className":1418},[618],[576,1420],{"className":1421,"style":1422},[622],"height:1.2251em;vertical-align:-0.345em;",[576,1424,1334],{"className":1425},[627],[576,1427,1429,1433,1503],{"className":1428},[627],[576,1430],{"className":1431},[1214,1432],"nulldelimiter",[576,1434,1436],{"className":1435},[1336],[576,1437,1439,1494],{"className":1438},[639,1372],[576,1440,1442,1491],{"className":1441},[643],[576,1443,1446,1465,1476],{"className":1444,"style":1445},[647],"height:0.8801em;",[576,1447,1449,1453],{"style":1448},"top:-2.655em;",[576,1450],{"className":1451,"style":1452},[654],"height:3em;",[576,1454,1456],{"className":1455},[659,660,661,662],[576,1457,1459,1462],{"className":1458},[627,662],[576,1460,604],{"className":1461},[627,662],[576,1463,681],{"className":1464},[627,631,662],[576,1466,1468,1471],{"style":1467},"top:-3.23em;",[576,1469],{"className":1470,"style":1452},[654],[576,1472],{"className":1473,"style":1475},[1474],"frac-line","border-bottom-width:0.04em;",[576,1477,1479,1482],{"style":1478},"top:-3.394em;",[576,1480],{"className":1481,"style":1452},[654],[576,1483,1485],{"className":1484},[659,660,661,662],[576,1486,1488],{"className":1487},[627,662],[576,1489,1340],{"className":1490},[627,631,662],[576,1492,1397],{"className":1493},[1396],[576,1495,1497],{"className":1496},[643],[576,1498,1501],{"className":1499,"style":1500},[647],"height:0.345em;",[576,1502],{},[576,1504],{"className":1505},[1221,1432],", die Parabel ist symmetrisch zur senkrechten Geraden durch ihn. Die ",[568,1508,1509],{},"Nullstellen"," findet man, indem man ",[576,1512,1514,1538],{"className":1513},[579],[576,1515,1517],{"className":1516},[583],[585,1518,1519],{"xmlns":587},[589,1520,1521,1535],{},[592,1522,1523,1525,1527,1529,1531,1533],{},[598,1524,1180],{},[683,1526,1184],{"stretchy":1183},[598,1528,600],{},[683,1530,1189],{"stretchy":1183},[683,1532,755],{},[602,1534,689],{},[606,1536,1537],{"encoding":608},"f(x) = 0",[576,1539,1541,1568],{"className":1540,"ariaHidden":614},[613],[576,1542,1544,1547,1550,1553,1556,1559,1562,1565],{"className":1543},[618],[576,1545],{"className":1546,"style":984},[622],[576,1548,1180],{"className":1549,"style":1210},[627,631],[576,1551,1184],{"className":1552},[1214],[576,1554,600],{"className":1555},[627,631],[576,1557,1189],{"className":1558},[1221],[576,1560],{"className":1561,"style":710},[709],[576,1563,755],{"className":1564},[714],[576,1566],{"className":1567,"style":710},[709],[576,1569,1571,1574],{"className":1570},[618],[576,1572],{"className":1573,"style":765},[622],[576,1575,689],{"className":1576},[627]," mit der abc-Formel oder (nach Teilen durch ",[576,1579,1581,1594],{"className":1580},[579],[576,1582,1584],{"className":1583},[583],[585,1585,1586],{"xmlns":587},[589,1587,1588,1592],{},[592,1589,1590],{},[598,1591,681],{},[606,1593,681],{"encoding":608},[576,1595,1597],{"className":1596,"ariaHidden":614},[613],[576,1598,1600,1603],{"className":1599},[618],[576,1601],{"className":1602,"style":800},[622],[576,1604,681],{"className":1605},[627,631],") mit der p-q-Formel löst. Es gibt zwei, eine oder keine.",[559,1608,1610],{"id":1609},"beispiele","Beispiele",[564,1612,1613,1770,1771,1827,1828,1827,1880,1936],{},[576,1614,1616,1659],{"className":1615},[579],[576,1617,1619],{"className":1618},[583],[585,1620,1621],{"xmlns":587},[589,1622,1623,1656],{},[592,1624,1625,1627,1629,1631,1633,1635,1637,1643,1646,1649,1651,1653],{},[598,1626,1180],{},[683,1628,1184],{"stretchy":1183},[598,1630,600],{},[683,1632,1189],{"stretchy":1183},[683,1634,755],{},[683,1636,1334],{},[595,1638,1639,1641],{},[598,1640,600],{},[602,1642,604],{},[683,1644,1645],{},"+",[602,1647,1648],{},"4",[598,1650,600],{},[683,1652,1334],{},[602,1654,1655],{},"3",[606,1657,1658],{"encoding":608},"f(x) = -x^2 + 4x - 3",[576,1660,1662,1689,1739,1761],{"className":1661,"ariaHidden":614},[613],[576,1663,1665,1668,1671,1674,1677,1680,1683,1686],{"className":1664},[618],[576,1666],{"className":1667,"style":984},[622],[576,1669,1180],{"className":1670,"style":1210},[627,631],[576,1672,1184],{"className":1673},[1214],[576,1675,600],{"className":1676},[627,631],[576,1678,1189],{"className":1679},[1221],[576,1681],{"className":1682,"style":710},[709],[576,1684,755],{"className":1685},[714],[576,1687],{"className":1688,"style":710},[709],[576,1690,1692,1696,1699,1728,1732,1736],{"className":1691},[618],[576,1693],{"className":1694,"style":1695},[622],"height:0.8974em;vertical-align:-0.0833em;",[576,1697,1334],{"className":1698},[627],[576,1700,1702,1705],{"className":1701},[627],[576,1703,600],{"className":1704},[627,631],[576,1706,1708],{"className":1707},[635],[576,1709,1711],{"className":1710},[639],[576,1712,1714],{"className":1713},[643],[576,1715,1717],{"className":1716,"style":623},[647],[576,1718,1719,1722],{"style":650},[576,1720],{"className":1721,"style":655},[654],[576,1723,1725],{"className":1724},[659,660,661,662],[576,1726,604],{"className":1727},[627,662],[576,1729],{"className":1730,"style":1731},[709],"margin-right:0.2222em;",[576,1733,1645],{"className":1734},[1735],"mbin",[576,1737],{"className":1738,"style":1731},[709],[576,1740,1742,1746,1749,1752,1755,1758],{"className":1741},[618],[576,1743],{"className":1744,"style":1745},[622],"height:0.7278em;vertical-align:-0.0833em;",[576,1747,1648],{"className":1748},[627],[576,1750,600],{"className":1751},[627,631],[576,1753],{"className":1754,"style":1731},[709],[576,1756,1334],{"className":1757},[1735],[576,1759],{"className":1760,"style":1731},[709],[576,1762,1764,1767],{"className":1763},[618],[576,1765],{"className":1766,"style":765},[622],[576,1768,1655],{"className":1769},[627],", also ",[576,1772,1774,1794],{"className":1773},[579],[576,1775,1777],{"className":1776},[583],[585,1778,1779],{"xmlns":587},[589,1780,1781,1791],{},[592,1782,1783,1785,1787,1789],{},[598,1784,681],{},[683,1786,755],{},[683,1788,1334],{},[602,1790,971],{},[606,1792,1793],{"encoding":608},"a = -1",[576,1795,1797,1815],{"className":1796,"ariaHidden":614},[613],[576,1798,1800,1803,1806,1809,1812],{"className":1799},[618],[576,1801],{"className":1802,"style":800},[622],[576,1804,681],{"className":1805},[627,631],[576,1807],{"className":1808,"style":710},[709],[576,1810,755],{"className":1811},[714],[576,1813],{"className":1814,"style":710},[709],[576,1816,1818,1821,1824],{"className":1817},[618],[576,1819],{"className":1820,"style":1745},[622],[576,1822,1334],{"className":1823},[627],[576,1825,971],{"className":1826},[627],", ",[576,1829,1831,1849],{"className":1830},[579],[576,1832,1834],{"className":1833},[583],[585,1835,1836],{"xmlns":587},[589,1837,1838,1846],{},[592,1839,1840,1842,1844],{},[598,1841,1340],{},[683,1843,755],{},[602,1845,1648],{},[606,1847,1848],{"encoding":608},"b = 4",[576,1850,1852,1871],{"className":1851,"ariaHidden":614},[613],[576,1853,1855,1859,1862,1865,1868],{"className":1854},[618],[576,1856],{"className":1857,"style":1858},[622],"height:0.6944em;",[576,1860,1340],{"className":1861},[627,631],[576,1863],{"className":1864,"style":710},[709],[576,1866,755],{"className":1867},[714],[576,1869],{"className":1870,"style":710},[709],[576,1872,1874,1877],{"className":1873},[618],[576,1875],{"className":1876,"style":765},[622],[576,1878,1648],{"className":1879},[627],[576,1881,1883,1903],{"className":1882},[579],[576,1884,1886],{"className":1885},[583],[585,1887,1888],{"xmlns":587},[589,1889,1890,1900],{},[592,1891,1892,1894,1896,1898],{},[598,1893,1194],{},[683,1895,755],{},[683,1897,1334],{},[602,1899,1655],{},[606,1901,1902],{"encoding":608},"c = -3",[576,1904,1906,1924],{"className":1905,"ariaHidden":614},[613],[576,1907,1909,1912,1915,1918,1921],{"className":1908},[618],[576,1910],{"className":1911,"style":800},[622],[576,1913,1194],{"className":1914},[627,631],[576,1916],{"className":1917,"style":710},[709],[576,1919,755],{"className":1920},[714],[576,1922],{"className":1923,"style":710},[709],[576,1925,1927,1930,1933],{"className":1926},[618],[576,1928],{"className":1929,"style":1745},[622],[576,1931,1334],{"className":1932},[627],[576,1934,1655],{"className":1935},[627],":",[827,1938,1939,1992,2066,2486],{},[830,1940,1941,1991],{},[576,1942,1944,1961],{"className":1943},[579],[576,1945,1947],{"className":1946},[583],[585,1948,1949],{"xmlns":587},[589,1950,1951,1959],{},[592,1952,1953,1955,1957],{},[598,1954,681],{},[683,1956,906],{},[602,1958,689],{},[606,1960,911],{"encoding":608},[576,1962,1964,1982],{"className":1963,"ariaHidden":614},[613],[576,1965,1967,1970,1973,1976,1979],{"className":1966},[618],[576,1968],{"className":1969,"style":867},[622],[576,1971,681],{"className":1972},[627,631],[576,1974],{"className":1975,"style":710},[709],[576,1977,906],{"className":1978},[714],[576,1980],{"className":1981,"style":710},[709],[576,1983,1985,1988],{"className":1984},[618],[576,1986],{"className":1987,"style":765},[622],[576,1989,689],{"className":1990},[627],": Die Parabel ist nach unten geöffnet und so breit wie die Normalparabel.",[830,1993,1994,1995,1302],{},"y-Achsenabschnitt: ",[576,1996,1998,2024],{"className":1997},[579],[576,1999,2001],{"className":2000},[583],[585,2002,2003],{"xmlns":587},[589,2004,2005,2021],{},[592,2006,2007,2009,2011,2013,2015,2017,2019],{},[598,2008,1180],{},[683,2010,1184],{"stretchy":1183},[602,2012,689],{},[683,2014,1189],{"stretchy":1183},[683,2016,755],{},[683,2018,1334],{},[602,2020,1655],{},[606,2022,2023],{"encoding":608},"f(0) = -3",[576,2025,2027,2054],{"className":2026,"ariaHidden":614},[613],[576,2028,2030,2033,2036,2039,2042,2045,2048,2051],{"className":2029},[618],[576,2031],{"className":2032,"style":984},[622],[576,2034,1180],{"className":2035,"style":1210},[627,631],[576,2037,1184],{"className":2038},[1214],[576,2040,689],{"className":2041},[627],[576,2043,1189],{"className":2044},[1221],[576,2046],{"className":2047,"style":710},[709],[576,2049,755],{"className":2050},[714],[576,2052],{"className":2053,"style":710},[709],[576,2055,2057,2060,2063],{"className":2056},[618],[576,2058],{"className":2059,"style":1745},[622],[576,2061,1334],{"className":2062},[627],[576,2064,1655],{"className":2065},[627],[830,2067,2068,2069,1770,2300,2393,2394,1302],{},"Nullstellen: ",[576,2070,2072,2130],{"className":2071},[579],[576,2073,2075],{"className":2074},[583],[585,2076,2077],{"xmlns":587},[589,2078,2079,2127],{},[592,2080,2081,2083,2089,2091,2093,2095,2097,2099,2101,2103,2105,2107,2109,2111,2113,2115,2117,2119,2121,2123,2125],{},[683,2082,1334],{},[595,2084,2085,2087],{},[598,2086,600],{},[602,2088,604],{},[683,2090,1645],{},[602,2092,1648],{},[598,2094,600],{},[683,2096,1334],{},[602,2098,1655],{},[683,2100,755],{},[683,2102,1334],{},[683,2104,1184],{"stretchy":1183},[598,2106,600],{},[683,2108,1334],{},[602,2110,971],{},[683,2112,1189],{"stretchy":1183},[683,2114,1184],{"stretchy":1183},[598,2116,600],{},[683,2118,1334],{},[602,2120,1655],{},[683,2122,1189],{"stretchy":1183},[683,2124,755],{},[602,2126,689],{},[606,2128,2129],{"encoding":608},"-x^2 + 4x - 3 = -(x - 1)(x - 3) = 0",[576,2131,2133,2180,2201,2219,2243,2270,2291],{"className":2132,"ariaHidden":614},[613],[576,2134,2136,2139,2142,2171,2174,2177],{"className":2135},[618],[576,2137],{"className":2138,"style":1695},[622],[576,2140,1334],{"className":2141},[627],[576,2143,2145,2148],{"className":2144},[627],[576,2146,600],{"className":2147},[627,631],[576,2149,2151],{"className":2150},[635],[576,2152,2154],{"className":2153},[639],[576,2155,2157],{"className":2156},[643],[576,2158,2160],{"className":2159,"style":623},[647],[576,2161,2162,2165],{"style":650},[576,2163],{"className":2164,"style":655},[654],[576,2166,2168],{"className":2167},[659,660,661,662],[576,2169,604],{"className":2170},[627,662],[576,2172],{"className":2173,"style":1731},[709],[576,2175,1645],{"className":2176},[1735],[576,2178],{"className":2179,"style":1731},[709],[576,2181,2183,2186,2189,2192,2195,2198],{"className":2182},[618],[576,2184],{"className":2185,"style":1745},[622],[576,2187,1648],{"className":2188},[627],[576,2190,600],{"className":2191},[627,631],[576,2193],{"className":2194,"style":1731},[709],[576,2196,1334],{"className":2197},[1735],[576,2199],{"className":2200,"style":1731},[709],[576,2202,2204,2207,2210,2213,2216],{"className":2203},[618],[576,2205],{"className":2206,"style":765},[622],[576,2208,1655],{"className":2209},[627],[576,2211],{"className":2212,"style":710},[709],[576,2214,755],{"className":2215},[714],[576,2217],{"className":2218,"style":710},[709],[576,2220,2222,2225,2228,2231,2234,2237,2240],{"className":2221},[618],[576,2223],{"className":2224,"style":984},[622],[576,2226,1334],{"className":2227},[627],[576,2229,1184],{"className":2230},[1214],[576,2232,600],{"className":2233},[627,631],[576,2235],{"className":2236,"style":1731},[709],[576,2238,1334],{"className":2239},[1735],[576,2241],{"className":2242,"style":1731},[709],[576,2244,2246,2249,2252,2255,2258,2261,2264,2267],{"className":2245},[618],[576,2247],{"className":2248,"style":984},[622],[576,2250,971],{"className":2251},[627],[576,2253,1189],{"className":2254},[1221],[576,2256,1184],{"className":2257},[1214],[576,2259,600],{"className":2260},[627,631],[576,2262],{"className":2263,"style":1731},[709],[576,2265,1334],{"className":2266},[1735],[576,2268],{"className":2269,"style":1731},[709],[576,2271,2273,2276,2279,2282,2285,2288],{"className":2272},[618],[576,2274],{"className":2275,"style":984},[622],[576,2277,1655],{"className":2278},[627],[576,2280,1189],{"className":2281},[1221],[576,2283],{"className":2284,"style":710},[709],[576,2286,755],{"className":2287},[714],[576,2289],{"className":2290,"style":710},[709],[576,2292,2294,2297],{"className":2293},[618],[576,2295],{"className":2296,"style":765},[622],[576,2298,689],{"className":2299},[627],[576,2301,2303,2325],{"className":2302},[579],[576,2304,2306],{"className":2305},[583],[585,2307,2308],{"xmlns":587},[589,2309,2310,2322],{},[592,2311,2312,2318,2320],{},[1323,2313,2314,2316],{},[598,2315,600],{},[602,2317,971],{},[683,2319,755],{},[602,2321,971],{},[606,2323,2324],{"encoding":608},"x_1 = 1",[576,2326,2328,2384],{"className":2327,"ariaHidden":614},[613],[576,2329,2331,2334,2375,2378,2381],{"className":2330},[618],[576,2332],{"className":2333,"style":1359},[622],[576,2335,2337,2340],{"className":2336},[627],[576,2338,600],{"className":2339},[627,631],[576,2341,2343],{"className":2342},[635],[576,2344,2346,2367],{"className":2345},[639,1372],[576,2347,2349,2364],{"className":2348},[643],[576,2350,2353],{"className":2351,"style":2352},[647],"height:0.3011em;",[576,2354,2355,2358],{"style":1382},[576,2356],{"className":2357,"style":655},[654],[576,2359,2361],{"className":2360},[659,660,661,662],[576,2362,971],{"className":2363},[627,662],[576,2365,1397],{"className":2366},[1396],[576,2368,2370],{"className":2369},[643],[576,2371,2373],{"className":2372,"style":1404},[647],[576,2374],{},[576,2376],{"className":2377,"style":710},[709],[576,2379,755],{"className":2380},[714],[576,2382],{"className":2383,"style":710},[709],[576,2385,2387,2390],{"className":2386},[618],[576,2388],{"className":2389,"style":765},[622],[576,2391,971],{"className":2392},[627]," und ",[576,2395,2397,2419],{"className":2396},[579],[576,2398,2400],{"className":2399},[583],[585,2401,2402],{"xmlns":587},[589,2403,2404,2416],{},[592,2405,2406,2412,2414],{},[1323,2407,2408,2410],{},[598,2409,600],{},[602,2411,604],{},[683,2413,755],{},[602,2415,1655],{},[606,2417,2418],{"encoding":608},"x_2 = 3",[576,2420,2422,2477],{"className":2421,"ariaHidden":614},[613],[576,2423,2425,2428,2468,2471,2474],{"className":2424},[618],[576,2426],{"className":2427,"style":1359},[622],[576,2429,2431,2434],{"className":2430},[627],[576,2432,600],{"className":2433},[627,631],[576,2435,2437],{"className":2436},[635],[576,2438,2440,2460],{"className":2439},[639,1372],[576,2441,2443,2457],{"className":2442},[643],[576,2444,2446],{"className":2445,"style":2352},[647],[576,2447,2448,2451],{"style":1382},[576,2449],{"className":2450,"style":655},[654],[576,2452,2454],{"className":2453},[659,660,661,662],[576,2455,604],{"className":2456},[627,662],[576,2458,1397],{"className":2459},[1396],[576,2461,2463],{"className":2462},[643],[576,2464,2466],{"className":2465,"style":1404},[647],[576,2467],{},[576,2469],{"className":2470,"style":710},[709],[576,2472,755],{"className":2473},[714],[576,2475],{"className":2476,"style":710},[709],[576,2478,2480,2483],{"className":2479},[618],[576,2481],{"className":2482,"style":765},[622],[576,2484,1655],{"className":2485},[627],[830,2487,2488,2489,2393,2708,1770,2846,2912],{},"Scheitelpunkt: ",[576,2490,2492,2537],{"className":2491},[579],[576,2493,2495],{"className":2494},[583],[585,2496,2497],{"xmlns":587},[589,2498,2499,2534],{},[592,2500,2501,2507,2509,2511,2530,2532],{},[1323,2502,2503,2505],{},[598,2504,600],{},[598,2506,1329],{},[683,2508,755],{},[683,2510,1334],{},[1336,2512,2513,2515],{},[602,2514,1648],{},[592,2516,2517,2519,2522,2524,2526,2528],{},[602,2518,604],{},[683,2520,2521],{},"⋅",[683,2523,1184],{"stretchy":1183},[683,2525,1334],{},[602,2527,971],{},[683,2529,1189],{"stretchy":1183},[683,2531,755],{},[602,2533,604],{},[606,2535,2536],{"encoding":608},"x_S = -\\frac{4}{2 \\cdot (-1)} = 2",[576,2538,2540,2595,2699],{"className":2539,"ariaHidden":614},[613],[576,2541,2543,2546,2586,2589,2592],{"className":2542},[618],[576,2544],{"className":2545,"style":1359},[622],[576,2547,2549,2552],{"className":2548},[627],[576,2550,600],{"className":2551},[627,631],[576,2553,2555],{"className":2554},[635],[576,2556,2558,2578],{"className":2557},[639,1372],[576,2559,2561,2575],{"className":2560},[643],[576,2562,2564],{"className":2563,"style":1379},[647],[576,2565,2566,2569],{"style":1382},[576,2567],{"className":2568,"style":655},[654],[576,2570,2572],{"className":2571},[659,660,661,662],[576,2573,1329],{"className":2574,"style":1392},[627,631,662],[576,2576,1397],{"className":2577},[1396],[576,2579,2581],{"className":2580},[643],[576,2582,2584],{"className":2583,"style":1404},[647],[576,2585],{},[576,2587],{"className":2588,"style":710},[709],[576,2590,755],{"className":2591},[714],[576,2593],{"className":2594,"style":710},[709],[576,2596,2598,2602,2605,2690,2693,2696],{"className":2597},[618],[576,2599],{"className":2600,"style":2601},[622],"height:1.3651em;vertical-align:-0.52em;",[576,2603,1334],{"className":2604},[627],[576,2606,2608,2611,2687],{"className":2607},[627],[576,2609],{"className":2610},[1214,1432],[576,2612,2614],{"className":2613},[1336],[576,2615,2617,2678],{"className":2616},[639,1372],[576,2618,2620,2675],{"className":2619},[643],[576,2621,2624,2653,2661],{"className":2622,"style":2623},[647],"height:0.8451em;",[576,2625,2626,2629],{"style":1448},[576,2627],{"className":2628,"style":1452},[654],[576,2630,2632],{"className":2631},[659,660,661,662],[576,2633,2635,2638,2641,2644,2647,2650],{"className":2634},[627,662],[576,2636,604],{"className":2637},[627,662],[576,2639,2521],{"className":2640},[1735,662],[576,2642,1184],{"className":2643},[1214,662],[576,2645,1334],{"className":2646},[627,662],[576,2648,971],{"className":2649},[627,662],[576,2651,1189],{"className":2652},[1221,662],[576,2654,2655,2658],{"style":1467},[576,2656],{"className":2657,"style":1452},[654],[576,2659],{"className":2660,"style":1475},[1474],[576,2662,2663,2666],{"style":1478},[576,2664],{"className":2665,"style":1452},[654],[576,2667,2669],{"className":2668},[659,660,661,662],[576,2670,2672],{"className":2671},[627,662],[576,2673,1648],{"className":2674},[627,662],[576,2676,1397],{"className":2677},[1396],[576,2679,2681],{"className":2680},[643],[576,2682,2685],{"className":2683,"style":2684},[647],"height:0.52em;",[576,2686],{},[576,2688],{"className":2689},[1221,1432],[576,2691],{"className":2692,"style":710},[709],[576,2694,755],{"className":2695},[714],[576,2697],{"className":2698,"style":710},[709],[576,2700,2702,2705],{"className":2701},[618],[576,2703],{"className":2704,"style":765},[622],[576,2706,604],{"className":2707},[627],[576,2709,2711,2750],{"className":2710},[579],[576,2712,2714],{"className":2713},[583],[585,2715,2716],{"xmlns":587},[589,2717,2718,2747],{},[592,2719,2720,2722,2724,2726,2728,2730,2732,2734,2736,2739,2741,2743,2745],{},[598,2721,1180],{},[683,2723,1184],{"stretchy":1183},[602,2725,604],{},[683,2727,1189],{"stretchy":1183},[683,2729,755],{},[683,2731,1334],{},[602,2733,1648],{},[683,2735,1645],{},[602,2737,2738],{},"8",[683,2740,1334],{},[602,2742,1655],{},[683,2744,755],{},[602,2746,971],{},[606,2748,2749],{"encoding":608},"f(2) = -4 + 8 - 3 = 1",[576,2751,2753,2780,2801,2819,2837],{"className":2752,"ariaHidden":614},[613],[576,2754,2756,2759,2762,2765,2768,2771,2774,2777],{"className":2755},[618],[576,2757],{"className":2758,"style":984},[622],[576,2760,1180],{"className":2761,"style":1210},[627,631],[576,2763,1184],{"className":2764},[1214],[576,2766,604],{"className":2767},[627],[576,2769,1189],{"className":2770},[1221],[576,2772],{"className":2773,"style":710},[709],[576,2775,755],{"className":2776},[714],[576,2778],{"className":2779,"style":710},[709],[576,2781,2783,2786,2789,2792,2795,2798],{"className":2782},[618],[576,2784],{"className":2785,"style":1745},[622],[576,2787,1334],{"className":2788},[627],[576,2790,1648],{"className":2791},[627],[576,2793],{"className":2794,"style":1731},[709],[576,2796,1645],{"className":2797},[1735],[576,2799],{"className":2800,"style":1731},[709],[576,2802,2804,2807,2810,2813,2816],{"className":2803},[618],[576,2805],{"className":2806,"style":1745},[622],[576,2808,2738],{"className":2809},[627],[576,2811],{"className":2812,"style":1731},[709],[576,2814,1334],{"className":2815},[1735],[576,2817],{"className":2818,"style":1731},[709],[576,2820,2822,2825,2828,2831,2834],{"className":2821},[618],[576,2823],{"className":2824,"style":765},[622],[576,2826,1655],{"className":2827},[627],[576,2829],{"className":2830,"style":710},[709],[576,2832,755],{"className":2833},[714],[576,2835],{"className":2836,"style":710},[709],[576,2838,2840,2843],{"className":2839},[618],[576,2841],{"className":2842,"style":765},[622],[576,2844,971],{"className":2845},[627],[576,2847,2849,2873],{"className":2848},[579],[576,2850,2852],{"className":2851},[583],[585,2853,2854],{"xmlns":587},[589,2855,2856,2870],{},[592,2857,2858,2860,2862,2864,2866,2868],{},[598,2859,1329],{},[683,2861,1184],{"stretchy":1183},[602,2863,604],{},[683,2865,962],{},[602,2867,971],{},[683,2869,1189],{"stretchy":1183},[606,2871,2872],{"encoding":608},"S(2 \\mid 1)",[576,2874,2876,2900],{"className":2875,"ariaHidden":614},[613],[576,2877,2879,2882,2885,2888,2891,2894,2897],{"className":2878},[618],[576,2880],{"className":2881,"style":984},[622],[576,2883,1329],{"className":2884,"style":1392},[627,631],[576,2886,1184],{"className":2887},[1214],[576,2889,604],{"className":2890},[627],[576,2892],{"className":2893,"style":710},[709],[576,2895,962],{"className":2896},[714],[576,2898],{"className":2899,"style":710},[709],[576,2901,2903,2906,2909],{"className":2902},[618],[576,2904],{"className":2905,"style":984},[622],[576,2907,971],{"className":2908},[627],[576,2910,1189],{"className":2911},[1221],". Er liegt genau zwischen den Nullstellen.",[559,2914,2916],{"id":2915},"typische-fehler","Typische Fehler",[827,2918,2919,3342,3401],{},[830,2920,2921,2393,2985,3060,3061,3162,3163,3312,3313,3341],{},[576,2922,2924,2944],{"className":2923},[579],[576,2925,2927],{"className":2926},[583],[585,2928,2929],{"xmlns":587},[589,2930,2931,2941],{},[592,2932,2933,2935],{},[683,2934,1334],{},[595,2936,2937,2939],{},[598,2938,600],{},[602,2940,604],{},[606,2942,2943],{"encoding":608},"-x^2",[576,2945,2947],{"className":2946,"ariaHidden":614},[613],[576,2948,2950,2953,2956],{"className":2949},[618],[576,2951],{"className":2952,"style":1695},[622],[576,2954,1334],{"className":2955},[627],[576,2957,2959,2962],{"className":2958},[627],[576,2960,600],{"className":2961},[627,631],[576,2963,2965],{"className":2964},[635],[576,2966,2968],{"className":2967},[639],[576,2969,2971],{"className":2970},[643],[576,2972,2974],{"className":2973,"style":623},[647],[576,2975,2976,2979],{"style":650},[576,2977],{"className":2978,"style":655},[654],[576,2980,2982],{"className":2981},[659,660,661,662],[576,2983,604],{"className":2984},[627,662],[576,2986,2988,3012],{"className":2987},[579],[576,2989,2991],{"className":2990},[583],[585,2992,2993],{"xmlns":587},[589,2994,2995,3009],{},[592,2996,2997,2999,3001,3003],{},[683,2998,1184],{"stretchy":1183},[683,3000,1334],{},[598,3002,600],{},[595,3004,3005,3007],{},[683,3006,1189],{"stretchy":1183},[602,3008,604],{},[606,3010,3011],{"encoding":608},"(-x)^2",[576,3013,3015],{"className":3014,"ariaHidden":614},[613],[576,3016,3018,3022,3025,3028,3031],{"className":3017},[618],[576,3019],{"className":3020,"style":3021},[622],"height:1.0641em;vertical-align:-0.25em;",[576,3023,1184],{"className":3024},[1214],[576,3026,1334],{"className":3027},[627],[576,3029,600],{"className":3030},[627,631],[576,3032,3034,3037],{"className":3033},[1221],[576,3035,1189],{"className":3036},[1221],[576,3038,3040],{"className":3039},[635],[576,3041,3043],{"className":3042},[639],[576,3044,3046],{"className":3045},[643],[576,3047,3049],{"className":3048,"style":623},[647],[576,3050,3051,3054],{"style":650},[576,3052],{"className":3053,"style":655},[654],[576,3055,3057],{"className":3056},[659,660,661,662],[576,3058,604],{"className":3059},[627,662]," verwechseln: Für ",[576,3062,3064,3094],{"className":3063},[579],[576,3065,3067],{"className":3066},[583],[585,3068,3069],{"xmlns":587},[589,3070,3071,3091],{},[592,3072,3073,3075,3077,3079,3081,3083,3085],{},[598,3074,1180],{},[683,3076,1184],{"stretchy":1183},[598,3078,600],{},[683,3080,1189],{"stretchy":1183},[683,3082,755],{},[683,3084,1334],{},[595,3086,3087,3089],{},[598,3088,600],{},[602,3090,604],{},[606,3092,3093],{"encoding":608},"f(x) = -x^2",[576,3095,3097,3124],{"className":3096,"ariaHidden":614},[613],[576,3098,3100,3103,3106,3109,3112,3115,3118,3121],{"className":3099},[618],[576,3101],{"className":3102,"style":984},[622],[576,3104,1180],{"className":3105,"style":1210},[627,631],[576,3107,1184],{"className":3108},[1214],[576,3110,600],{"className":3111},[627,631],[576,3113,1189],{"className":3114},[1221],[576,3116],{"className":3117,"style":710},[709],[576,3119,755],{"className":3120},[714],[576,3122],{"className":3123,"style":710},[709],[576,3125,3127,3130,3133],{"className":3126},[618],[576,3128],{"className":3129,"style":1695},[622],[576,3131,1334],{"className":3132},[627],[576,3134,3136,3139],{"className":3135},[627],[576,3137,600],{"className":3138},[627,631],[576,3140,3142],{"className":3141},[635],[576,3143,3145],{"className":3144},[639],[576,3146,3148],{"className":3147},[643],[576,3149,3151],{"className":3150,"style":623},[647],[576,3152,3153,3156],{"style":650},[576,3154],{"className":3155,"style":655},[654],[576,3157,3159],{"className":3158},[659,660,661,662],[576,3160,604],{"className":3161},[627,662]," ist ",[576,3164,3166,3211],{"className":3165},[579],[576,3167,3169],{"className":3168},[583],[585,3170,3171],{"xmlns":587},[589,3172,3173,3208],{},[592,3174,3175,3177,3179,3181,3183,3185,3187,3189,3191,3193,3195,3201,3203,3205],{},[598,3176,1180],{},[683,3178,1184],{"stretchy":1183},[683,3180,1334],{},[602,3182,1655],{},[683,3184,1189],{"stretchy":1183},[683,3186,755],{},[683,3188,1334],{},[683,3190,1184],{"stretchy":1183},[683,3192,1334],{},[602,3194,1655],{},[595,3196,3197,3199],{},[683,3198,1189],{"stretchy":1183},[602,3200,604],{},[683,3202,755],{},[683,3204,1334],{},[602,3206,3207],{},"9",[606,3209,3210],{"encoding":608},"f(-3) = -(-3)^2 = -9",[576,3212,3214,3244,3300],{"className":3213,"ariaHidden":614},[613],[576,3215,3217,3220,3223,3226,3229,3232,3235,3238,3241],{"className":3216},[618],[576,3218],{"className":3219,"style":984},[622],[576,3221,1180],{"className":3222,"style":1210},[627,631],[576,3224,1184],{"className":3225},[1214],[576,3227,1334],{"className":3228},[627],[576,3230,1655],{"className":3231},[627],[576,3233,1189],{"className":3234},[1221],[576,3236],{"className":3237,"style":710},[709],[576,3239,755],{"className":3240},[714],[576,3242],{"className":3243,"style":710},[709],[576,3245,3247,3250,3253,3256,3259,3262,3291,3294,3297],{"className":3246},[618],[576,3248],{"className":3249,"style":3021},[622],[576,3251,1334],{"className":3252},[627],[576,3254,1184],{"className":3255},[1214],[576,3257,1334],{"className":3258},[627],[576,3260,1655],{"className":3261},[627],[576,3263,3265,3268],{"className":3264},[1221],[576,3266,1189],{"className":3267},[1221],[576,3269,3271],{"className":3270},[635],[576,3272,3274],{"className":3273},[639],[576,3275,3277],{"className":3276},[643],[576,3278,3280],{"className":3279,"style":623},[647],[576,3281,3282,3285],{"style":650},[576,3283],{"className":3284,"style":655},[654],[576,3286,3288],{"className":3287},[659,660,661,662],[576,3289,604],{"className":3290},[627,662],[576,3292],{"className":3293,"style":710},[709],[576,3295,755],{"className":3296},[714],[576,3298],{"className":3299,"style":710},[709],[576,3301,3303,3306,3309],{"className":3302},[618],[576,3304],{"className":3305,"style":1745},[622],[576,3307,1334],{"className":3308},[627],[576,3310,3207],{"className":3311},[627],", nicht ",[576,3314,3316,3329],{"className":3315},[579],[576,3317,3319],{"className":3318},[583],[585,3320,3321],{"xmlns":587},[589,3322,3323,3327],{},[592,3324,3325],{},[602,3326,3207],{},[606,3328,3207],{"encoding":608},[576,3330,3332],{"className":3331,"ariaHidden":614},[613],[576,3333,3335,3338],{"className":3334},[618],[576,3336],{"className":3337,"style":765},[622],[576,3339,3207],{"className":3340},[627],". Erst quadrieren, dann das Minus anwenden.",[830,3343,3344,3372,3373,1302],{},[576,3345,3347,3360],{"className":3346},[579],[576,3348,3350],{"className":3349},[583],[585,3351,3352],{"xmlns":587},[589,3353,3354,3358],{},[592,3355,3356],{},[598,3357,1340],{},[606,3359,1340],{"encoding":608},[576,3361,3363],{"className":3362,"ariaHidden":614},[613],[576,3364,3366,3369],{"className":3365},[618],[576,3367],{"className":3368,"style":1858},[622],[576,3370,1340],{"className":3371},[627,631]," für den y-Achsenabschnitt halten, wie bei der linearen Funktion. Bei der Parabel ist es ",[576,3374,3376,3389],{"className":3375},[579],[576,3377,3379],{"className":3378},[583],[585,3380,3381],{"xmlns":587},[589,3382,3383,3387],{},[592,3384,3385],{},[598,3386,1194],{},[606,3388,1194],{"encoding":608},[576,3390,3392],{"className":3391,"ariaHidden":614},[613],[576,3393,3395,3398],{"className":3394},[618],[576,3396],{"className":3397,"style":800},[622],[576,3399,1194],{"className":3400},[627,631],[830,3402,3403,3404,3432,3433,3472],{},"Aus „",[576,3405,3407,3420],{"className":3406},[579],[576,3408,3410],{"className":3409},[583],[585,3411,3412],{"xmlns":587},[589,3413,3414,3418],{},[592,3415,3416],{},[598,3417,681],{},[606,3419,681],{"encoding":608},[576,3421,3423],{"className":3422,"ariaHidden":614},[613],[576,3424,3426,3429],{"className":3425},[618],[576,3427],{"className":3428,"style":800},[622],[576,3430,681],{"className":3431},[627,631]," ist groß“ schließen, dass die Parabel breit ist. Es ist umgekehrt: Großes ",[576,3434,3436,3454],{"className":3435},[579],[576,3437,3439],{"className":3438},[583],[585,3440,3441],{"xmlns":587},[589,3442,3443,3451],{},[592,3444,3445,3447,3449],{},[598,3446,962],{"mathvariant":685},[598,3448,681],{},[598,3450,962],{"mathvariant":685},[606,3452,3453],{"encoding":608},"|a|",[576,3455,3457],{"className":3456,"ariaHidden":614},[613],[576,3458,3460,3463,3466,3469],{"className":3459},[618],[576,3461],{"className":3462,"style":984},[622],[576,3464,962],{"className":3465},[627],[576,3467,681],{"className":3468},[627,631],[576,3470,962],{"className":3471},[627]," macht sie schmal.",{"title":3474,"searchDepth":3475,"depth":3475,"links":3476},"",2,[3477,3478,3479],{"id":561,"depth":3475,"text":562},{"id":1609,"depth":3475,"text":1610},{"id":2915,"depth":3475,"text":2916},[3481,3483,3486,3494,3497,3500,3502,3505],{"lhs":3482,"rhs":1194},"a*0^2 + b*0 + c",{"lhs":3484,"rhs":3485},"a*(-b\u002F(2*a) + h)^2 + b*(-b\u002F(2*a) + h) + c","a*(-b\u002F(2*a) - h)^2 + b*(-b\u002F(2*a) - h) + c",{"lhs":3487,"rhs":3488,"where":3489},"a*x^2 + b*x + c","-3",{"a":3490,"b":3491,"c":3492,"x":3493},-1,4,-3,0,{"lhs":3487,"rhs":689,"where":3495},{"a":3490,"b":3491,"c":3492,"x":3496},1,{"lhs":3487,"rhs":689,"where":3498},{"a":3490,"b":3491,"c":3492,"x":3499},3,{"lhs":3487,"rhs":971,"where":3501},{"a":3490,"b":3491,"c":3492,"x":3475},{"lhs":3503,"rhs":3504},"-x^2 + 4*x - 3","-(x - 1)*(x - 3)",{"lhs":3506,"rhs":3507},"-(-3)^2","-9","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a \\neq 0\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\">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 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