76:@0.058783:0.510692:0.077690:0.510692:0.077690:0.494068:0.058783:0.494068:0.000000:0.000000
Tema:@0.047190:0.135475:0.083321:0.135475:0.083321:0.113749:0.047190:0.113749:0.000000:0.000000:0.000000:0.000000
Actividad resuelta:@0.115209:0.614102:0.272331:0.614102:0.272331:0.595665:0.115209:0.595665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Resolvamos:@0.115209:0.633949:0.206647:0.633949:0.206647:0.617325:0.115209:0.617325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 gráficamente la ecuación cuadrática  * :@0.206647:0.633949:0.520035:0.634237:0.520035:0.617848:0.206647:0.617560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.115209:0.650545:0.122672:0.650545:0.122672:0.634184:0.115209:0.634184:0.000000
2:@0.122672:0.644498:0.127915:0.644498:0.127915:0.634943:0.122672:0.634943:0.000000
 – 4 = 0:@0.127915:0.650545:0.182240:0.650545:0.182240:0.634156:0.127915:0.634156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
* :@0.115219:0.674264:0.126460:0.674264:0.126460:0.657875:0.115219:0.657875:0.000000:0.000000
Construimos:@0.126460:0.674264:0.223960:0.674264:0.223960:0.657640:0.126460:0.657640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 el gráfico de la función::@0.223960:0.674264:0.398286:0.674264:0.398286:0.657875:0.223960:0.657875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   f x:@0.115219:0.697983:0.142215:0.697983:0.142215:0.681622:0.115219:0.681622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) =   – 4:@0.129869:0.697983:0.205126:0.697994:0.205126:0.681605:0.129869:0.681594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.166153:0.697983:0.173616:0.697983:0.173616:0.681622:0.166153:0.681622:0.000000
2:@0.173604:0.691947:0.178847:0.691947:0.178847:0.682392:0.173604:0.682392:0.000000
Localizamos :@0.520035:0.634237:0.617849:0.634237:0.617849:0.617613:0.520035:0.617613:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el vértice V::@0.617849:0.634237:0.700239:0.634237:0.700239:0.617848:0.617849:0.617848:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   :@0.508795:0.729624:0.520902:0.729624:0.520902:0.713235:0.508795:0.713235:0.000000:0.000000:0.000000
x:@0.524977:0.666244:0.532441:0.666244:0.532441:0.649883:0.524977:0.649883:0.000000
b:@0.566237:0.657724:0.575506:0.657724:0.575506:0.641363:0.566237:0.641363:0.000000
a:@0.570844:0.677170:0.580113:0.677170:0.580113:0.660808:0.570844:0.660808:0.000000
f:@0.523522:0.698192:0.528221:0.698192:0.528221:0.681831:0.523522:0.681831:0.000000
V:@0.613246:0.721219:0.622367:0.721219:0.622367:0.704858:0.613246:0.704858:0.000000
–:@0.549541:0.666258:0.558755:0.666258:0.558755:0.649869:0.549541:0.649869:0.000000
2:@0.561685:0.677184:0.570678:0.677184:0.570678:0.660795:0.561685:0.660795:0.000000
–:@0.597601:0.666258:0.606815:0.666258:0.606815:0.649869:0.597601:0.649869:0.000000
0:@0.616139:0.657738:0.625132:0.657738:0.625132:0.641349:0.616139:0.641349:0.000000
21:@0.609745:0.677184:0.634548:0.677184:0.634548:0.660795:0.609745:0.660795:0.000000:0.000000
0;:@0.648479:0.666258:0.661213:0.666258:0.661213:0.649869:0.648479:0.649869:0.000000:0.000000
0:@0.538743:0.698206:0.547736:0.698206:0.547736:0.681817:0.538743:0.681817:0.000000
0 –4 –4:@0.576169:0.698206:0.657564:0.698206:0.657564:0.681817:0.576169:0.681817:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por lo que::@0.523079:0.721233:0.607699:0.721233:0.607699:0.704844:0.523079:0.704844:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.547938:0.721233:0.551145:0.721233:0.551145:0.704844:0.547938:0.704844:0.000000
. ..:@0.550979:0.721233:0.573663:0.721233:0.573663:0.704844:0.550979:0.704844:0.000000:0.000000:0.000000:0.000000
.:@0.610205:0.721233:0.613412:0.721233:0.613412:0.704844:0.610205:0.704844:0.000000
0,–4:@0.632300:0.721233:0.664954:0.721233:0.664954:0.704844:0.632300:0.704844:0.000000:0.000000:0.000000:0.000000
2:@0.592093:0.688640:0.597304:0.688640:0.597304:0.679142:0.592093:0.679142:0.000000
() ():@0.532307:0.701320:0.591846:0.701320:0.591846:0.681386:0.532307:0.681386:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.625859:0.724344:0.631995:0.724344:0.631995:0.704410:0.625859:0.704410:0.000000
):@0.665865:0.724344:0.672001:0.724344:0.672001:0.704410:0.665865:0.704410:0.000000
=:@0.536495:0.666921:0.546611:0.666921:0.546611:0.651349:0.536495:0.651349:0.000000
=:@0.584554:0.666921:0.594671:0.666921:0.594671:0.651349:0.584554:0.651349:0.000000
⋅:@0.620304:0.677847:0.624910:0.677847:0.624910:0.662274:0.620304:0.662274:0.000000
=:@0.635801:0.666921:0.645918:0.666921:0.645918:0.651349:0.635801:0.651349:0.000000
=:@0.557070:0.698864:0.567187:0.698864:0.567187:0.683292:0.557070:0.683292:0.000000
=:@0.626339:0.698864:0.636456:0.698864:0.636456:0.683292:0.626339:0.683292:0.000000
* :@0.508788:0.753345:0.520029:0.753345:0.520029:0.736956:0.508788:0.736956:0.000000:0.000000
Observamos:@0.521853:0.753345:0.618506:0.753345:0.618506:0.736721:0.521853:0.736721:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 que la parábola corta al eje de las :@0.618506:0.753345:0.885171:0.753345:0.885171:0.736956:0.618506:0.736956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.881081:0.753345:0.885117:0.753345:0.885117:0.736956:0.881081:0.736956:0.000000
     en los puntos  (–2, 0)  y   (2, 0).:@0.508788:0.769941:0.761392:0.769941:0.761392:0.753552:0.508788:0.753552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.520895:0.769941:0.528358:0.769941:0.528358:0.753580:0.520895:0.753580:0.000000
A:@0.635992:0.769941:0.645888:0.769941:0.645888:0.753580:0.635992:0.753580:0.000000
B:@0.714346:0.769941:0.723192:0.769941:0.723192:0.753580:0.714346:0.753580:0.000000
   Por tanto, las soluciones de la ecuación :@0.508788:0.793660:0.812881:0.793660:0.812881:0.777271:0.508788:0.777271:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.813120:0.793660:0.820584:0.793660:0.820584:0.777299:0.813120:0.777299:0.000000
2:@0.820562:0.787618:0.825804:0.787618:0.825804:0.778063:0.820562:0.778063:0.000000
 – 4 = 0 :@0.825805:0.793665:0.885124:0.793665:0.885124:0.777276:0.825805:0.777276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.881088:0.793665:0.885124:0.793665:0.885124:0.777276:0.881088:0.777276:0.000000
 :@0.881088:0.793665:0.885124:0.793665:0.885124:0.777276:0.881088:0.777276:0.000000
 :@0.881088:0.793665:0.885124:0.793665:0.885124:0.777276:0.881088:0.777276:0.000000
   :@0.508795:0.810261:0.520902:0.810261:0.520902:0.793872:0.508795:0.793872:0.000000:0.000000:0.000000
son:   = –2     = 2.:@0.520902:0.810261:0.670802:0.810261:0.670802:0.793872:0.520902:0.793872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.554698:0.810261:0.562161:0.810261:0.562161:0.793900:0.554698:0.793900:0.000000
1:@0.562153:0.813425:0.567395:0.813425:0.567395:0.803870:0.562153:0.803870:0.000000
  y x:@0.604657:0.810261:0.634307:0.810261:0.634307:0.793900:0.604657:0.793900:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.634305:0.813425:0.639548:0.813425:0.639548:0.803870:0.634305:0.803870:0.000000
* :@0.508786:0.833980:0.520027:0.833980:0.520027:0.817591:0.508786:0.817591:0.000000:0.000000
Escribimos:@0.520027:0.833980:0.602638:0.833980:0.602638:0.817356:0.520027:0.817356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 el conjunto solución::@0.602638:0.833980:0.759807:0.833980:0.759807:0.817591:0.602638:0.817591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   S:@0.508786:0.857699:0.526808:0.857699:0.526808:0.841338:0.508786:0.841338:0.000000:0.000000:0.000000:0.000000
 = {–2, 2}  o    = –2       = 2:@0.526808:0.857699:0.731464:0.857711:0.731464:0.841322:0.526808:0.841310:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.617122:0.857699:0.624585:0.857699:0.624585:0.841338:0.617122:0.841338:0.000000
1:@0.624585:0.860874:0.629828:0.860874:0.629828:0.851320:0.624585:0.851320:0.000000
y x:@0.675159:0.857711:0.698175:0.857711:0.698175:0.841349:0.675159:0.841349:0.000000:0.000000:0.000000
2:@0.698174:0.860874:0.703416:0.860874:0.703416:0.851320:0.698174:0.851320:0.000000
* :@0.508785:0.881430:0.520025:0.881430:0.520025:0.865041:0.508785:0.865041:0.000000:0.000000
Verificamos:@0.520025:0.881430:0.608902:0.881430:0.608902:0.864806:0.520025:0.864806:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 en la ecuación::@0.608902:0.881430:0.722361:0.881430:0.722361:0.865041:0.608902:0.865041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   (2)  – 4 = 0;  0 = 0:@0.508785:0.905149:0.647538:0.905159:0.647538:0.888770:0.508785:0.888760:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.539654:0.899111:0.544897:0.899111:0.544897:0.889557:0.539654:0.889557:0.000000
   (–2)  – 4 = 0;  0 = 0:@0.508796:0.928878:0.656752:0.928883:0.656752:0.912494:0.508796:0.912489:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.548868:0.922836:0.554111:0.922836:0.554111:0.913281:0.548868:0.913281:0.000000
Una ecuación cuadrática es aquella que puede escribirse en la forma :@0.115200:0.172476:0.621566:0.172476:0.621566:0.156087:0.115200:0.156087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax:@0.624264:0.172472:0.639304:0.172472:0.639304:0.156110:0.624264:0.156110:0.000000:0.000000
bx c:@0.659630:0.172472:0.695678:0.172472:0.695678:0.156110:0.659630:0.156110:0.000000:0.000000:0.000000:0.000000
a bc:@0.772095:0.172472:0.805400:0.172472:0.805400:0.156110:0.772095:0.156110:0.000000:0.000000:0.000000:0.000000
a:@0.840883:0.172472:0.849243:0.172472:0.849243:0.156110:0.840883:0.156110:0.000000
0, donde ,,:@0.710187:0.172472:0.796924:0.172472:0.796924:0.156083:0.710187:0.156083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.722502:0.172472:0.725394:0.172472:0.725394:0.156083:0.722502:0.156083:0.000000
.:@0.768688:0.172472:0.771580:0.172472:0.771580:0.156083:0.768688:0.156083:0.000000
,:@0.836429:0.172472:0.839321:0.172472:0.839321:0.156083:0.836429:0.156083:0.000000
0.:@0.863336:0.172472:0.874172:0.172472:0.874172:0.156083:0.863336:0.156083:0.000000:0.000000
2:@0.640788:0.164811:0.645489:0.164811:0.645489:0.155312:0.640788:0.155312:0.000000
:@0.823698:0.173343:0.835697:0.173343:0.835697:0.156594:0.823698:0.156594:0.000000
+:@0.648677:0.173149:0.657801:0.173149:0.657801:0.157576:0.648677:0.157576:0.000000
+ =:@0.677479:0.173149:0.707893:0.173149:0.707893:0.157576:0.677479:0.157576:0.000000:0.000000:0.000000
∈:@0.808823:0.173149:0.820673:0.173149:0.820673:0.157576:0.808823:0.157576:0.000000
≠:@0.851934:0.173149:0.861058:0.173149:0.861058:0.157576:0.851934:0.157576:0.000000
La ecuación cuadrática puede tener solución real, que pueden ser dos soluciones iguales (a) o dos solu-:@0.115209:0.271192:0.879919:0.271192:0.879919:0.254803:0.115209:0.254803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ciones reales diferentes (b), y puede no tener soluciones reales (c).:@0.115209:0.287789:0.597046:0.287789:0.597046:0.271400:0.115209:0.271400:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Analizamos:@0.115209:0.453379:0.203754:0.453379:0.203754:0.436755:0.115209:0.436755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 los gráficos que corresponden a las siguientes ecuaciones::@0.203754:0.453379:0.634328:0.453379:0.634328:0.436990:0.203754:0.436990:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a) :@0.115209:0.477098:0.133931:0.477098:0.133931:0.460197:0.115209:0.460197:0.000000:0.000000:0.000000
x:@0.148452:0.477098:0.155916:0.477098:0.155916:0.460737:0.148452:0.460737:0.000000
2:@0.155729:0.471053:0.160972:0.471053:0.160972:0.461498:0.155729:0.461498:0.000000
 = 0, con una solución real   = 0. La parábola corta al eje de las   en un único punto con abscisa   = 0.:@0.160864:0.477100:0.879892:0.477100:0.879892:0.460712:0.160864:0.460712:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.351498:0.477100:0.358961:0.477100:0.358961:0.460739:0.351498:0.460739:0.000000
x:@0.606553:0.477100:0.614016:0.477100:0.614016:0.460739:0.606553:0.460739:0.000000
x:@0.842115:0.477100:0.849579:0.477100:0.849579:0.460739:0.842115:0.460739:0.000000
b) :@0.115200:0.497265:0.135231:0.497265:0.135231:0.480364:0.115200:0.480364:0.000000:0.000000:0.000000
x:@0.148444:0.497265:0.155907:0.497265:0.155907:0.480904:0.148444:0.480904:0.000000
2:@0.155914:0.491214:0.161156:0.491214:0.161156:0.481659:0.155914:0.481659:0.000000
 – 1 = 0, con dos soluciones reales   = –1  y    = 1. La parábola corta al eje de las   en dos puntos :@0.161156:0.497261:0.883946:0.497261:0.883946:0.480872:0.161156:0.480872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.415973:0.497261:0.423436:0.497261:0.423436:0.480900:0.415973:0.480900:0.000000
1:@0.423426:0.500425:0.428669:0.500425:0.428669:0.490870:0.423426:0.490870:0.000000
x:@0.491729:0.497261:0.499192:0.497261:0.499192:0.480900:0.491729:0.480900:0.000000
2:@0.499187:0.500425:0.504430:0.500425:0.504430:0.490870:0.499187:0.490870:0.000000
x:@0.761955:0.497261:0.769418:0.497261:0.769418:0.480900:0.761955:0.480900:0.000000
con abscisas   = –1  y    = 1.:@0.148444:0.513858:0.362189:0.513858:0.362189:0.497469:0.148444:0.497469:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.244010:0.513858:0.251473:0.513858:0.251473:0.497496:0.244010:0.497496:0.000000
1:@0.251478:0.517021:0.256720:0.517021:0.256720:0.507467:0.251478:0.507467:0.000000
x:@0.318231:0.513858:0.325694:0.513858:0.325694:0.497496:0.318231:0.497496:0.000000
2:@0.325693:0.517021:0.330935:0.517021:0.330935:0.507467:0.325693:0.507467:0.000000
c) :@0.115204:0.534022:0.132839:0.534022:0.132839:0.517122:0.115204:0.517122:0.000000:0.000000:0.000000
x:@0.148447:0.534022:0.155910:0.534022:0.155910:0.517661:0.148447:0.517661:0.000000
2:@0.155914:0.527970:0.161156:0.527970:0.161156:0.518415:0.155914:0.518415:0.000000
 + 1 = 0, sin soluciones reales. La parábola no corta al eje de las   .:@0.161156:0.534017:0.638466:0.534017:0.638466:0.517628:0.161156:0.517628:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.623761:0.534017:0.631224:0.534017:0.631224:0.517656:0.623761:0.517656:0.000000
El método gráfico puede emplearse para resolver una ecuación cuadrática, para ello :@0.115215:0.554182:0.737900:0.554182:0.737900:0.537793:0.115215:0.537793:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dibujas:@0.738287:0.554182:0.794289:0.554182:0.794289:0.537558:0.738287:0.537558:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la parábola :@0.794289:0.554182:0.884031:0.554182:0.884031:0.537793:0.794289:0.537793:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y :@0.115215:0.570778:0.127359:0.570778:0.127359:0.554389:0.115215:0.554389:0.000000:0.000000
buscas:@0.127359:0.570778:0.179731:0.570778:0.179731:0.554154:0.127359:0.554154:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 los puntos de corte con el eje de las  .:@0.179731:0.570778:0.461524:0.570778:0.461524:0.554389:0.179731:0.554389:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.450855:0.570778:0.458318:0.570778:0.458318:0.554417:0.450855:0.554417:0.000000
Ecuación de segundo grado, soluciones gráficas:@0.115891:0.141978:0.824813:0.141978:0.824813:0.101242:0.115891:0.101242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.4.1.58. Reconocer los ceros de la función cuadrática como la solución de la ecuación de segundo grado con una incógnita.:@0.125388:0.074999:0.706923:0.074999:0.706923:0.064570:0.125388:0.064570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
20:@0.043057:0.122645:0.087454:0.122645:0.087454:0.065614:0.043057:0.065614:0.000000:0.000000
Resolver una ecuación cuadrática significa hallar los valores de la incógnita que hacen verdadera :@0.142316:0.204702:0.851608:0.204702:0.851608:0.188314:0.142316:0.188314:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la igualdad. Gráficamente las soluciones reales de esta ecuación corresponden a los puntos de :@0.142316:0.221299:0.836221:0.221299:0.836221:0.204910:0.142316:0.204910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
corte de la parábola con el eje  .:@0.142316:0.237895:0.378079:0.237895:0.378079:0.221506:0.142316:0.221506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.367409:0.237895:0.374873:0.237895:0.374873:0.221534:0.367409:0.221534:0.000000
x:@0.133338:0.727356:0.140123:0.727356:0.140123:0.712482:0.133338:0.712482:0.000000
–3:@0.170663:0.727356:0.187214:0.727356:0.187214:0.712457:0.170663:0.712457:0.000000:0.000000
–2:@0.212862:0.727356:0.229413:0.727356:0.229413:0.712457:0.212862:0.712457:0.000000:0.000000
–1:@0.255061:0.727356:0.271612:0.727356:0.271612:0.712457:0.255061:0.712457:0.000000:0.000000
0:@0.301448:0.727356:0.309624:0.727356:0.309624:0.712457:0.301448:0.712457:0.000000
1:@0.343648:0.727356:0.351823:0.727356:0.351823:0.712457:0.343648:0.712457:0.000000
2:@0.385847:0.727356:0.394022:0.727356:0.394022:0.712457:0.385847:0.712457:0.000000
3:@0.428046:0.727356:0.436222:0.727356:0.436222:0.712457:0.428046:0.712457:0.000000
f x:@0.125582:0.754552:0.142217:0.754552:0.142217:0.739678:0.125582:0.739678:0.000000:0.000000:0.000000
( ):@0.129854:0.755168:0.147796:0.755168:0.147796:0.741010:0.129854:0.741010:0.000000:0.000000:0.000000
5:@0.174800:0.754552:0.182976:0.754552:0.182976:0.739653:0.174800:0.739653:0.000000
0:@0.217000:0.754552:0.225175:0.754552:0.225175:0.739653:0.217000:0.739653:0.000000
–3:@0.255011:0.754552:0.271562:0.754552:0.271562:0.739653:0.255011:0.739653:0.000000:0.000000
–4:@0.297210:0.754552:0.313762:0.754552:0.313762:0.739653:0.297210:0.739653:0.000000:0.000000
–3:@0.339409:0.754552:0.355961:0.754552:0.355961:0.739653:0.339409:0.739653:0.000000:0.000000
0:@0.385797:0.754552:0.393972:0.754552:0.393972:0.739653:0.385797:0.739653:0.000000
5:@0.427996:0.754552:0.436171:0.754552:0.436171:0.739653:0.427996:0.739653:0.000000
y:@0.308416:0.311504:0.313857:0.311504:0.313857:0.299605:0.308416:0.299605:0.000000
x:@0.378575:0.387032:0.384003:0.387032:0.384003:0.375133:0.378575:0.375133:0.000000
1:@0.294036:0.372518:0.300576:0.372518:0.300576:0.360599:0.294036:0.360599:0.000000
2:@0.291074:0.351144:0.297614:0.351144:0.297614:0.339225:0.291074:0.339225:0.000000
3:@0.290122:0.329770:0.296662:0.329770:0.296662:0.317851:0.290122:0.317851:0.000000
1:@0.328840:0.399605:0.335380:0.399605:0.335380:0.387686:0.328840:0.387686:0.000000
2:@0.357561:0.399605:0.364101:0.399605:0.364101:0.387686:0.357561:0.387686:0.000000
–1 0:@0.265905:0.399605:0.299034:0.399605:0.299034:0.387686:0.265905:0.387686:0.000000:0.000000:0.000000:0.000000
–2:@0.238833:0.399605:0.252074:0.399605:0.252074:0.387686:0.238833:0.387686:0.000000:0.000000
Soluciones reales iguales Soluciones reales diferentes:@0.210302:0.429215:0.612775:0.429215:0.612775:0.412826:0.210302:0.412826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.515387:0.312741:0.520828:0.312741:0.520828:0.300842:0.515387:0.300842:0.000000
x:@0.568793:0.366835:0.574221:0.366835:0.574221:0.354936:0.568793:0.354936:0.000000
1:@0.498031:0.351064:0.504571:0.351064:0.504571:0.339144:0.498031:0.339144:0.000000
2:@0.498031:0.328432:0.504571:0.328432:0.504571:0.316513:0.498031:0.316513:0.000000
1:@0.535798:0.378151:0.542338:0.378151:0.542338:0.366232:0.535798:0.366232:0.000000
2:@0.564518:0.378151:0.571058:0.378151:0.571058:0.366232:0.564518:0.366232:0.000000
–1 0:@0.472862:0.378151:0.505992:0.378151:0.505992:0.366232:0.472862:0.366232:0.000000:0.000000:0.000000:0.000000
–1:@0.492751:0.394104:0.505992:0.394104:0.505992:0.382184:0.492751:0.382184:0.000000:0.000000
–2:@0.445790:0.378151:0.459032:0.378151:0.459032:0.366232:0.445790:0.366232:0.000000:0.000000
y:@0.722977:0.311187:0.728419:0.311187:0.728419:0.299288:0.722977:0.299288:0.000000
x:@0.776384:0.388395:0.781812:0.388395:0.781812:0.376496:0.776384:0.376496:0.000000
1:@0.705622:0.372624:0.712162:0.372624:0.712162:0.360705:0.705622:0.360705:0.000000
2:@0.705622:0.349992:0.712162:0.349992:0.712162:0.338073:0.705622:0.338073:0.000000
3:@0.704670:0.328618:0.711210:0.328618:0.711210:0.316699:0.704670:0.316699:0.000000
1:@0.743388:0.399711:0.749929:0.399711:0.749929:0.387792:0.743388:0.387792:0.000000
2:@0.772109:0.399711:0.778649:0.399711:0.778649:0.387792:0.772109:0.387792:0.000000
–1 0:@0.680453:0.399711:0.713583:0.399711:0.713583:0.387792:0.680453:0.387792:0.000000:0.000000:0.000000:0.000000
–2:@0.653381:0.399711:0.666622:0.399711:0.666622:0.387792:0.653381:0.387792:0.000000:0.000000
Soluciones imaginarias:@0.635193:0.429215:0.802864:0.429215:0.802864:0.412826:0.635193:0.412826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.215063:0.799149:0.221603:0.799149:0.221603:0.787230:0.215063:0.787230:0.000000
1:@0.249265:0.825170:0.255805:0.825170:0.255805:0.813251:0.249265:0.813251:0.000000
2:@0.275626:0.825170:0.282166:0.825170:0.282166:0.813251:0.275626:0.813251:0.000000
B:@0.285356:0.811893:0.292124:0.811893:0.292124:0.799974:0.285356:0.799974:0.000000
V:@0.233853:0.907146:0.240674:0.907146:0.240674:0.895227:0.233853:0.895227:0.000000
A:@0.176372:0.811893:0.184212:0.811893:0.184212:0.799974:0.176372:0.799974:0.000000
3:@0.302926:0.825170:0.309466:0.825170:0.309466:0.813251:0.302926:0.813251:0.000000
–1:@0.207705:0.840238:0.220947:0.840238:0.220947:0.828319:0.207705:0.828319:0.000000:0.000000
–1 0:@0.190739:0.825170:0.223278:0.825170:0.223278:0.813251:0.190739:0.813251:0.000000:0.000000:0.000000:0.000000
–2:@0.207705:0.861904:0.220947:0.861904:0.220947:0.849985:0.207705:0.849985:0.000000:0.000000
–2:@0.164739:0.825170:0.177980:0.825170:0.177980:0.813251:0.164739:0.813251:0.000000:0.000000
–3:@0.207705:0.882302:0.220947:0.882302:0.220947:0.870383:0.207705:0.870383:0.000000:0.000000
–4:@0.207705:0.903978:0.220947:0.903978:0.220947:0.892059:0.207705:0.892059:0.000000:0.000000
–3:@0.137895:0.825170:0.151136:0.825170:0.151136:0.813251:0.137895:0.813251:0.000000:0.000000
x:@0.325884:0.811320:0.331311:0.811320:0.331311:0.799421:0.325884:0.799421:0.000000
y:@0.231574:0.780571:0.237015:0.780571:0.237015:0.768672:0.231574:0.768672:0.000000