105:@0.890754:0.963104:0.932133:0.963104:0.932133:0.941283:0.890754:0.941283:0.000000:0.000000:0.000000
Matemática:@0.795130:0.956142:0.879896:0.956142:0.879896:0.943479:0.795130:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
10.º EGB:@0.820728:0.967458:0.879897:0.967458:0.879897:0.954794:0.820728:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DUA:@0.748004:0.068322:0.791647:0.068322:0.791647:0.048070:0.748004:0.048070:0.000000:0.000000:0.000000
. Representación:@0.791647:0.067693:0.923937:0.067693:0.923937:0.050792:0.791647:0.050792:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desplazamiento vertical de la función cuadrática de la forma  ( ) = :@0.096359:0.100407:0.611319:0.100407:0.611319:0.083506:0.096359:0.083506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.568344:0.100407:0.587898:0.100407:0.587898:0.083506:0.568344:0.083506:0.000000:0.000000:0.000000
ax :@0.611135:0.100407:0.632788:0.100407:0.632788:0.083506:0.611135:0.083506:0.000000:0.000000:0.000000
2 + :@0.632603:0.100407:0.656799:0.100407:0.656799:0.083506:0.632603:0.083506:0.000000:0.000000:0.000000:0.000000
c:@0.656615:0.100407:0.664538:0.100407:0.664538:0.083506:0.656615:0.083506:0.000000
Trazamos y analizamos la gráfica de las siguientes funciones cuadráticas:  :@0.096378:0.124126:0.639200:0.124126:0.639200:0.107737:0.096378:0.107737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.096378:0.140722:0.113423:0.140722:0.113423:0.125329:0.096378:0.125329:0.000000:0.000000:0.000000
( ) =  2 + 3 ( ) =  2 – 2.:@0.101077:0.140722:0.279198:0.140722:0.279198:0.124333:0.101077:0.124333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.137361:0.140722:0.148141:0.140722:0.148141:0.125329:0.137361:0.125329:0.000000:0.000000
, g x:@0.181458:0.140722:0.209726:0.140722:0.209726:0.125329:0.181458:0.125329:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.233663:0.140722:0.244444:0.140722:0.244444:0.125329:0.233663:0.125329:0.000000:0.000000
f(x):@0.180382:0.196348:0.195812:0.196348:0.195812:0.185517:0.180382:0.185517:0.000000:0.000000:0.000000:0.000000
0:@0.195895:0.334486:0.201519:0.334486:0.201519:0.324236:0.195895:0.324236:0.000000
x:@0.321463:0.330431:0.326714:0.330431:0.326714:0.319600:0.321463:0.319600:0.000000
Dos unidades :@0.224537:0.352064:0.289909:0.352064:0.289909:0.341814:0.224537:0.341814:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hacia abajo.:@0.224537:0.360715:0.278477:0.360715:0.278477:0.350464:0.224537:0.350464:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Vértice (0, – ): (0, :@0.224537:0.370775:0.303176:0.370775:0.303176:0.360524:0.224537:0.360524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.277589:0.370775:0.282384:0.370775:0.282384:0.361147:0.277589:0.361147:0.000000
–2):@0.303174:0.371125:0.319967:0.371125:0.319967:0.359206:0.303174:0.359206:0.000000:0.000000:0.000000
Tres unidades :@0.224537:0.210688:0.290013:0.210688:0.290013:0.200438:0.224537:0.200438:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hacia arriba.:@0.224537:0.219339:0.279455:0.219339:0.279455:0.209088:0.224537:0.209088:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Vértice (0,  ): (0, 3):@0.224537:0.227989:0.306092:0.227989:0.306092:0.217738:0.224537:0.217738:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.271826:0.227989:0.276621:0.227989:0.276621:0.218361:0.271826:0.218361:0.000000
y:@0.247945:0.314898:0.252625:0.314898:0.252625:0.305270:0.247945:0.305270:0.000000
 =   – 2:@0.252625:0.314898:0.288928:0.314901:0.288928:0.304651:0.252625:0.304647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.264542:0.314898:0.269210:0.314898:0.269210:0.305270:0.264542:0.305270:0.000000
2:@0.269214:0.311119:0.272493:0.311119:0.272493:0.305143:0.269214:0.305143:0.000000
y:@0.148176:0.231305:0.152856:0.231305:0.152856:0.221678:0.148176:0.221678:0.000000
 =   + 3:@0.152856:0.231305:0.190265:0.231302:0.190265:0.221051:0.152856:0.221055:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.164773:0.231305:0.169441:0.231305:0.169441:0.221678:0.164773:0.221678:0.000000
2:@0.169445:0.227520:0.172724:0.227520:0.172724:0.221544:0.169445:0.221544:0.000000
y:@0.212533:0.292087:0.217212:0.292087:0.217212:0.282459:0.212533:0.282459:0.000000
 = :@0.217212:0.292087:0.229130:0.292087:0.229130:0.281837:0.217212:0.281837:0.000000:0.000000:0.000000
x:@0.229125:0.292436:0.234553:0.292436:0.234553:0.281241:0.229125:0.281241:0.000000
2:@0.234553:0.288038:0.238366:0.288038:0.238366:0.281089:0.234553:0.281089:0.000000
1:@0.194282:0.313719:0.199203:0.313719:0.199203:0.304750:0.194282:0.304750:0.000000
–1:@0.189239:0.344366:0.199203:0.344366:0.199203:0.335397:0.189239:0.335397:0.000000:0.000000
–2:@0.189239:0.359693:0.199203:0.359693:0.199203:0.350724:0.189239:0.350724:0.000000:0.000000
2:@0.194282:0.298392:0.199203:0.298392:0.199203:0.289423:0.194282:0.289423:0.000000
3:@0.194282:0.283065:0.199203:0.283065:0.199203:0.274096:0.194282:0.274096:0.000000
4:@0.194282:0.267738:0.199203:0.267738:0.199203:0.258769:0.194282:0.258769:0.000000
5:@0.194282:0.252411:0.199203:0.252411:0.199203:0.243442:0.194282:0.243442:0.000000
6:@0.194282:0.237084:0.199203:0.237084:0.199203:0.228114:0.194282:0.228114:0.000000
7:@0.194282:0.221756:0.199203:0.221756:0.199203:0.212787:0.194282:0.212787:0.000000
–1:@0.179154:0.335442:0.189118:0.335442:0.189118:0.326473:0.179154:0.326473:0.000000:0.000000
1:@0.222510:0.335442:0.227431:0.335442:0.227431:0.326473:0.222510:0.326473:0.000000
2:@0.242932:0.335442:0.247853:0.335442:0.247853:0.326473:0.242932:0.326473:0.000000
3:@0.263354:0.335442:0.268275:0.335442:0.268275:0.326473:0.263354:0.326473:0.000000
4:@0.283776:0.335442:0.288697:0.335442:0.288697:0.326473:0.283776:0.326473:0.000000
–2:@0.158742:0.335442:0.168706:0.335442:0.168706:0.326473:0.158742:0.326473:0.000000:0.000000
–3:@0.138320:0.335442:0.148284:0.335442:0.148284:0.326473:0.138320:0.326473:0.000000:0.000000
–4:@0.117898:0.335442:0.127862:0.335442:0.127862:0.326473:0.117898:0.326473:0.000000:0.000000
Graficamos la función  =  2.:@0.360985:0.174346:0.550320:0.174346:0.550320:0.159447:0.360985:0.159447:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y:@0.505675:0.174346:0.515492:0.174346:0.515492:0.160352:0.505675:0.160352:0.000000:0.000000
x :@0.532814:0.174346:0.542614:0.174346:0.542614:0.160352:0.532814:0.160352:0.000000:0.000000
La gráfica de   =  2 + 3 indica que la gráfica inicial   =  2 se desplazó hacia arriba 3 :@0.360985:0.192992:0.911464:0.192992:0.911464:0.178093:0.360985:0.178093:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.449052:0.192992:0.455854:0.192992:0.455854:0.178998:0.449052:0.178998:0.000000
x :@0.473176:0.192992:0.482976:0.192992:0.482976:0.178998:0.473176:0.178998:0.000000:0.000000
y:@0.695529:0.192992:0.702330:0.192992:0.702330:0.178998:0.695529:0.178998:0.000000
x :@0.719652:0.192992:0.729452:0.192992:0.729452:0.178998:0.719652:0.178998:0.000000:0.000000
unidades.:@0.360985:0.208080:0.425296:0.208080:0.425296:0.193181:0.360985:0.193181:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El dominio son los   y el recorrido [3, + ∞).:@0.360985:0.226725:0.645171:0.226725:0.645171:0.211826:0.360985:0.211826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.486460:0.227253:0.498556:0.227253:0.498556:0.211248:0.486460:0.211248:0.000000
La gráfica de la función   =  2 – 2 indica que la gráfica   =  2 se desplazó hacia :@0.360985:0.245371:0.884107:0.245371:0.884107:0.230472:0.360985:0.230472:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.518675:0.245371:0.525477:0.245371:0.525477:0.231377:0.518675:0.231377:0.000000
x :@0.542799:0.245371:0.552599:0.245371:0.552599:0.231377:0.542799:0.231377:0.000000:0.000000
y:@0.721763:0.245371:0.728564:0.245371:0.728564:0.231377:0.721763:0.231377:0.000000
x :@0.745886:0.245371:0.755686:0.245371:0.755686:0.231377:0.745886:0.231377:0.000000:0.000000
abajo 2 unidades.:@0.360985:0.260459:0.477764:0.260459:0.477764:0.245560:0.360985:0.245560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El dominio son los   y el recorrido [–2, + ∞).:@0.360985:0.279104:0.653547:0.279104:0.653547:0.264205:0.360985:0.264205:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.486460:0.279633:0.498556:0.279633:0.498556:0.263627:0.486460:0.263627:0.000000
En forma general, en la función  ( ) = :@0.360985:0.297750:0.609036:0.297750:0.609036:0.282851:0.360985:0.282851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.571779:0.297750:0.587275:0.297750:0.587275:0.283756:0.571779:0.283756:0.000000:0.000000:0.000000
ax :@0.609036:0.297750:0.627263:0.297750:0.627263:0.283756:0.609036:0.283756:0.000000:0.000000:0.000000
2 +  , con   > 0 se puede decir: si   > 0, la :@0.627263:0.297750:0.902099:0.297750:0.902099:0.282851:0.627263:0.282851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.649376:0.297750:0.656345:0.297750:0.656345:0.283756:0.649376:0.283756:0.000000
a:@0.691960:0.297750:0.700387:0.297750:0.700387:0.283756:0.691960:0.283756:0.000000
c:@0.848223:0.297750:0.855192:0.297750:0.855192:0.283756:0.848223:0.283756:0.000000
función se desplaza   unidades hacia arriba.:@0.360985:0.312838:0.651453:0.312838:0.651453:0.297939:0.360985:0.297939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.495741:0.312838:0.502710:0.312838:0.502710:0.298844:0.495741:0.298844:0.000000
Si   < 0, la función se desplaza   unidades hacia abajo. :@0.360985:0.331484:0.722515:0.331484:0.722515:0.316585:0.360985:0.316585:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.375928:0.331484:0.382897:0.331484:0.382897:0.317490:0.375928:0.317490:0.000000
c:@0.564560:0.331484:0.571529:0.331484:0.571529:0.317490:0.564560:0.317490:0.000000
El dominio son todos los números reales  .:@0.360985:0.350129:0.648623:0.350129:0.648623:0.335230:0.360985:0.335230:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.633778:0.350657:0.645873:0.350657:0.645873:0.334652:0.633778:0.334652:0.000000
El recorrido: si   > 0, y ≥  , si   < 0, y ≤  .:@0.360985:0.368775:0.624130:0.368775:0.624130:0.353876:0.360985:0.353876:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.456874:0.368775:0.465300:0.368775:0.465300:0.354781:0.456874:0.354781:0.000000
c:@0.522074:0.368775:0.529043:0.368775:0.529043:0.354781:0.522074:0.354781:0.000000
a:@0.549046:0.368775:0.557472:0.368775:0.557472:0.354781:0.549046:0.354781:0.000000
c:@0.614246:0.368775:0.621215:0.368775:0.621215:0.354781:0.614246:0.354781:0.000000
Eje de simetría, eje  . :@0.360985:0.387421:0.501486:0.387421:0.501486:0.372522:0.360985:0.372522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.488100:0.387421:0.494902:0.387421:0.494902:0.373427:0.488100:0.373427:0.000000
Vértice (0,  ).:@0.360985:0.406067:0.444043:0.406067:0.444043:0.391168:0.360985:0.391168:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.429720:0.406067:0.436689:0.406067:0.436689:0.392073:0.429720:0.392073:0.000000
Desplazamiento horizontal de la función cuadrática  de la forma  ( ) = (  + )2:@0.096359:0.444608:0.704318:0.444608:0.704318:0.427707:0.096359:0.427707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.606007:0.444608:0.625927:0.444608:0.625927:0.427707:0.606007:0.427707:0.000000:0.000000:0.000000
x  h:@0.655632:0.444608:0.692635:0.444608:0.692635:0.427707:0.655632:0.427707:0.000000:0.000000:0.000000:0.000000
Trazamos y analizamos la gráfica de las siguientes funciones cuadráticas:  :@0.096359:0.468327:0.632358:0.468327:0.632358:0.451938:0.096359:0.451938:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.096359:0.484923:0.113405:0.484923:0.113405:0.469530:0.096359:0.469530:0.000000:0.000000:0.000000
( ) = (  + 4)2,  ( ) = ( – 2)2.:@0.101058:0.484923:0.291950:0.486182:0.291950:0.469793:0.101058:0.468534:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.142226:0.484923:0.149689:0.484923:0.149689:0.469530:0.142226:0.469530:0.000000
g x:@0.195131:0.484923:0.216747:0.484923:0.216747:0.469530:0.195131:0.469530:0.000000:0.000000:0.000000
x :@0.245568:0.484923:0.256348:0.484923:0.256348:0.469530:0.245568:0.469530:0.000000:0.000000
f(x):@0.239202:0.518648:0.253316:0.518648:0.253316:0.508740:0.239202:0.508740:0.000000:0.000000:0.000000:0.000000
0:@0.253391:0.621098:0.258536:0.621098:0.258536:0.611722:0.253391:0.611722:0.000000
x:@0.380341:0.617389:0.385144:0.617389:0.385144:0.607481:0.380341:0.607481:0.000000
Dos unidades :@0.327426:0.596109:0.387224:0.596109:0.387224:0.586733:0.327426:0.586733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a la derecha:@0.327426:0.604022:0.377948:0.604022:0.377948:0.594646:0.327426:0.594646:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cuatro :@0.115632:0.592193:0.146123:0.592189:0.146123:0.582813:0.115632:0.582816:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
unidades :@0.115634:0.600102:0.156697:0.600102:0.156697:0.590725:0.115634:0.590725:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a la izquierda:@0.115634:0.608014:0.170572:0.608014:0.170572:0.598638:0.115634:0.598638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.326226:0.526918:0.330506:0.526918:0.330506:0.518112:0.326226:0.518112:0.000000
 = (  – 2):@0.330506:0.526918:0.366299:0.526918:0.366299:0.517542:0.330506:0.517542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.344201:0.526918:0.348471:0.526918:0.348471:0.518112:0.344201:0.518112:0.000000
2:@0.366302:0.523456:0.369302:0.523456:0.369302:0.517990:0.366302:0.517990:0.000000
y:@0.135776:0.526916:0.140056:0.526916:0.140056:0.518110:0.135776:0.518110:0.000000
 = (  + 4):@0.140056:0.526916:0.176861:0.526916:0.176861:0.517540:0.140056:0.517540:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.153751:0.526916:0.158021:0.526916:0.158021:0.518110:0.153751:0.518110:0.000000
2:@0.176861:0.523456:0.179860:0.523456:0.179860:0.517990:0.176861:0.517990:0.000000
y:@0.208392:0.528526:0.212673:0.528526:0.212673:0.519719:0.208392:0.519719:0.000000
 = :@0.212673:0.528526:0.223574:0.528526:0.223574:0.519149:0.212673:0.519149:0.000000:0.000000:0.000000
x:@0.223573:0.529062:0.229001:0.529062:0.229001:0.517867:0.223573:0.517867:0.000000
2:@0.229001:0.524664:0.232814:0.524664:0.232814:0.517715:0.229001:0.517715:0.000000
1:@0.252114:0.602026:0.256616:0.602026:0.256616:0.593821:0.252114:0.593821:0.000000
–1:@0.247502:0.630059:0.256616:0.630059:0.256616:0.621855:0.247502:0.621855:0.000000:0.000000
2:@0.252114:0.588005:0.256616:0.588005:0.256616:0.579801:0.252114:0.579801:0.000000
3:@0.252114:0.573985:0.256616:0.573985:0.256616:0.565781:0.252114:0.565781:0.000000
4:@0.252114:0.559965:0.256616:0.559965:0.256616:0.551760:0.252114:0.551760:0.000000
5:@0.252114:0.545944:0.256616:0.545944:0.256616:0.537740:0.252114:0.537740:0.000000
6:@0.252114:0.531924:0.256616:0.531924:0.256616:0.523720:0.252114:0.523720:0.000000
–1:@0.238111:0.621959:0.247225:0.621959:0.247225:0.613754:0.238111:0.613754:0.000000:0.000000
1:@0.277769:0.621959:0.282271:0.621959:0.282271:0.613754:0.277769:0.613754:0.000000
2:@0.296450:0.621959:0.300952:0.621959:0.300952:0.613754:0.296450:0.613754:0.000000
3:@0.315131:0.621959:0.319632:0.621959:0.319632:0.613754:0.315131:0.613754:0.000000
4:@0.333811:0.621959:0.338313:0.621959:0.338313:0.613754:0.333811:0.613754:0.000000
5:@0.352492:0.621959:0.356994:0.621959:0.356994:0.613754:0.352492:0.613754:0.000000
–2:@0.219439:0.621959:0.228554:0.621959:0.228554:0.613754:0.219439:0.613754:0.000000:0.000000
–3:@0.200759:0.621959:0.209873:0.621959:0.209873:0.613754:0.200759:0.613754:0.000000:0.000000
–4:@0.182078:0.621959:0.191192:0.621959:0.191192:0.613754:0.182078:0.613754:0.000000:0.000000
–5:@0.163397:0.621959:0.172511:0.621959:0.172511:0.613754:0.163397:0.613754:0.000000:0.000000
–6:@0.144716:0.621959:0.153831:0.621959:0.153831:0.613754:0.144716:0.613754:0.000000:0.000000
Graficamos la función y =  .:@0.412034:0.528959:0.602564:0.528959:0.602564:0.514060:0.412034:0.514060:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.585087:0.528959:0.594887:0.528959:0.594887:0.514965:0.585087:0.514965:0.000000:0.000000
2:@0.594883:0.523462:0.599650:0.523462:0.599650:0.514775:0.594883:0.514775:0.000000
La gráfica de   = (  + 4)  indica que la gráfica inicial   =   se desplazó hacia :@0.412039:0.547605:0.914734:0.547611:0.914734:0.532712:0.412039:0.532706:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.500107:0.547605:0.506908:0.547605:0.506908:0.533611:0.500107:0.533611:0.000000
x:@0.528670:0.547605:0.535454:0.547605:0.535454:0.533611:0.528670:0.533611:0.000000
2:@0.565383:0.542114:0.570149:0.542114:0.570149:0.533428:0.565383:0.533428:0.000000
y:@0.752413:0.547611:0.759214:0.547611:0.759214:0.533617:0.752413:0.533617:0.000000
x :@0.776536:0.547611:0.786337:0.547611:0.786337:0.533617:0.776536:0.533617:0.000000:0.000000
2:@0.786337:0.542114:0.791103:0.542114:0.791103:0.533428:0.786337:0.533428:0.000000
la izquierda 4 unidades y la gráfica de   = (  – 2)  indica que se desplazó :@0.412029:0.562699:0.890821:0.562699:0.890821:0.547800:0.412029:0.547800:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.663965:0.562699:0.670767:0.562699:0.670767:0.548705:0.663965:0.548705:0.000000
x:@0.692528:0.562699:0.699313:0.562699:0.699313:0.548705:0.692528:0.548705:0.000000
2:@0.727645:0.557201:0.732411:0.557201:0.732411:0.548515:0.727645:0.548515:0.000000
hacia la derecha 2 unidades.:@0.412038:0.577786:0.599696:0.577786:0.599696:0.562887:0.412038:0.562887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En forma general, en la función  ( ) = (  +  ) , si   > 0, se desplaza la gráfica  :@0.412038:0.596432:0.914040:0.596438:0.914040:0.581539:0.412038:0.581533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.622832:0.596432:0.638327:0.596432:0.638327:0.582438:0.622832:0.582438:0.000000:0.000000:0.000000
x:@0.664528:0.596432:0.671313:0.596432:0.671313:0.582438:0.664528:0.582438:0.000000
h:@0.688635:0.596432:0.697279:0.596432:0.697279:0.582438:0.688635:0.582438:0.000000
2:@0.701712:0.590940:0.706478:0.590940:0.706478:0.582254:0.701712:0.582254:0.000000
h:@0.726480:0.596438:0.735124:0.596438:0.735124:0.582445:0.726480:0.582445:0.000000
y:@0.412038:0.611526:0.418839:0.611526:0.418839:0.597532:0.412038:0.597532:0.000000
 =   hacia la izquierda   unidades. Si   < 0, se desplaza la función inicial a :@0.418839:0.611526:0.911510:0.611526:0.911510:0.596627:0.418839:0.596627:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.436161:0.611526:0.445961:0.611526:0.445961:0.597532:0.436161:0.597532:0.000000:0.000000
2:@0.445956:0.606029:0.450722:0.606029:0.450722:0.597342:0.445956:0.597342:0.000000
h:@0.572913:0.611526:0.581557:0.611526:0.581557:0.597532:0.572913:0.597532:0.000000
h:@0.668148:0.611526:0.676793:0.611526:0.676793:0.597532:0.668148:0.597532:0.000000
la derecha   unidades.:@0.412041:0.626614:0.561338:0.626614:0.561338:0.611715:0.412041:0.611715:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.484713:0.626614:0.493357:0.626614:0.493357:0.612620:0.484713:0.612620:0.000000
Ejemplo :@0.096359:0.675509:0.159308:0.675509:0.159308:0.658871:0.096359:0.658871:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Graficamos la función   =  2 – 2 – 3. Luego, determinamos la concavidad, el eje de :@0.096359:0.699228:0.716519:0.699228:0.716519:0.682839:0.096359:0.682839:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.260863:0.699228:0.268344:0.699228:0.268344:0.683835:0.260863:0.683835:0.000000
x :@0.288430:0.699228:0.299211:0.699228:0.299211:0.683835:0.288430:0.683835:0.000000:0.000000
x :@0.332214:0.699228:0.342995:0.699228:0.342995:0.683835:0.332214:0.683835:0.000000:0.000000
simetría, vértice, dominio y recorrido de la función.:@0.096341:0.715824:0.466898:0.715824:0.466898:0.699435:0.096341:0.699435:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reconocemos en la función   =  2 – 2  – 3, los coeficientes:   = 1,   = –2 y   = –3. :@0.103311:0.756815:0.633975:0.756815:0.633975:0.741916:0.103311:0.741916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.288442:0.756815:0.295244:0.756815:0.295244:0.742821:0.288442:0.742821:0.000000
x :@0.312063:0.756815:0.321863:0.756815:0.321863:0.742821:0.312063:0.742821:0.000000:0.000000
x:@0.349706:0.756815:0.356490:0.756815:0.356490:0.742821:0.349706:0.742821:0.000000
a:@0.492217:0.756815:0.500643:0.756815:0.500643:0.742821:0.492217:0.742821:0.000000
b:@0.531719:0.756815:0.540145:0.756815:0.540145:0.742821:0.531719:0.742821:0.000000
c:@0.587387:0.756815:0.594356:0.756815:0.594356:0.742821:0.587387:0.742821:0.000000
Determinamos el vértice de la parábola: :@0.103311:0.781659:0.372268:0.781659:0.372268:0.766760:0.103311:0.766760:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=−:@0.388233:0.782953:0.412115:0.782953:0.412115:0.767380:0.388233:0.767380:0.000000:0.000000
==:@0.438542:0.782953:0.476871:0.782953:0.476871:0.767380:0.438542:0.767380:0.000000:0.000000
x:@0.376348:0.782275:0.383812:0.782275:0.383812:0.766882:0.376348:0.766882:0.000000
b:@0.419856:0.773313:0.429125:0.773313:0.429125:0.757920:0.419856:0.757920:0.000000
a:@0.424460:0.792765:0.433729:0.792765:0.433729:0.777372:0.424460:0.777372:0.000000
2:@0.415301:0.792765:0.424294:0.792765:0.424294:0.776376:0.415301:0.776376:0.000000
2:@0.453409:0.773317:0.462402:0.773317:0.462402:0.756928:0.453409:0.756928:0.000000
2:@0.453409:0.792765:0.462402:0.792765:0.462402:0.776376:0.453409:0.776376:0.000000
1:@0.479005:0.782268:0.487998:0.782268:0.487998:0.765879:0.479005:0.765879:0.000000
f:@0.107604:0.814701:0.112303:0.814701:0.112303:0.798340:0.107604:0.798340:0.000000
b:@0.143726:0.805822:0.152995:0.805822:0.152995:0.789461:0.143726:0.789461:0.000000
2:@0.139175:0.825157:0.148167:0.825157:0.148167:0.808768:0.139175:0.808768:0.000000
a:@0.148333:0.825157:0.157602:0.825157:0.157602:0.808795:0.148333:0.808795:0.000000
=:@0.171839:0.815379:0.181955:0.815379:0.181955:0.799806:0.171839:0.799806:0.000000
f:@0.185143:0.814701:0.189842:0.814701:0.189842:0.798340:0.185143:0.798340:0.000000
(1) 1 2(1) 3:@0.192367:0.814701:0.292392:0.814701:0.292392:0.798312:0.192367:0.798312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.211255:0.815379:0.221372:0.815379:0.221372:0.799806:0.211255:0.799806:0.000000
=:@0.294751:0.815379:0.304868:0.815379:0.304868:0.799806:0.294751:0.799806:0.000000
4; (1, 4):@0.322042:0.814701:0.387340:0.814701:0.387340:0.798312:0.322042:0.798312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
V:@0.335494:0.814701:0.344616:0.814701:0.344616:0.798340:0.335494:0.798340:0.000000
Determinamos la ecuación del eje de simetría. :@0.103311:0.848291:0.414832:0.848291:0.414832:0.833392:0.103311:0.833392:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=−:@0.427768:0.849444:0.451650:0.849444:0.451650:0.833871:0.427768:0.833871:0.000000:0.000000
==:@0.478079:0.849444:0.516409:0.849444:0.516409:0.833871:0.478079:0.833871:0.000000:0.000000
x:@0.415886:0.848766:0.423349:0.848766:0.423349:0.833373:0.415886:0.833373:0.000000
b:@0.459393:0.839804:0.468663:0.839804:0.468663:0.824411:0.459393:0.824411:0.000000
a:@0.463995:0.859256:0.473264:0.859256:0.473264:0.843863:0.463995:0.843863:0.000000
2:@0.454837:0.859256:0.463829:0.859256:0.463829:0.842867:0.454837:0.842867:0.000000
2:@0.492947:0.839808:0.501940:0.839808:0.501940:0.823419:0.492947:0.823419:0.000000
2:@0.492947:0.859256:0.501940:0.859256:0.501940:0.842867:0.492947:0.842867:0.000000
1:@0.518543:0.848759:0.527535:0.848759:0.527535:0.832370:0.518543:0.832370:0.000000
 ,   = 1:@0.527393:0.848291:0.569927:0.848291:0.569927:0.833392:0.527393:0.833392:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.537646:0.848291:0.544430:0.848291:0.544430:0.834297:0.537646:0.834297:0.000000
Tomamos valores de   a los dos lados del eje de simetría. Elaboramos una tabla :@0.103306:0.875738:0.631838:0.875738:0.631838:0.860839:0.103306:0.860839:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.244125:0.875738:0.250910:0.875738:0.250910:0.861744:0.244125:0.861744:0.000000
de valores y graficamos. :@0.103306:0.890825:0.265685:0.890825:0.265685:0.875926:0.103306:0.875926:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f(x):@0.746416:0.748062:0.760679:0.748062:0.760679:0.738050:0.746416:0.738050:0.000000:0.000000:0.000000:0.000000
0:@0.760756:0.835093:0.765955:0.835093:0.765955:0.825617:0.760756:0.825617:0.000000
x:@0.888158:0.831345:0.893012:0.831345:0.893012:0.821332:0.888158:0.821332:0.000000
eje de simetría :@0.800320:0.845138:0.800320:0.796920:0.787694:0.796920:0.787694:0.845138:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.800320:0.796920:0.800320:0.793681:0.788461:0.793681:0.788461:0.796920:0.000000
 = 1:@0.800320:0.793681:0.800320:0.781511:0.787694:0.781511:0.787694:0.793681:0.000000:0.000000:0.000000:0.000000
decreciente:@0.690913:0.846071:0.741075:0.846071:0.741075:0.836595:0.690913:0.836595:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(–∞, 1]:@0.690913:0.854067:0.718871:0.854067:0.718871:0.844591:0.690913:0.844591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
creciente:@0.841046:0.808135:0.880244:0.808135:0.880244:0.798660:0.841046:0.798660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[1, +∞):@0.841046:0.816132:0.870027:0.816132:0.870027:0.806656:0.841046:0.806656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1 > 0:@0.799653:0.747706:0.821069:0.747706:0.821069:0.738231:0.799653:0.738231:0.000000:0.000000:0.000000:0.000000:0.000000
cóncava hacia arriba:@0.799653:0.755703:0.886211:0.755703:0.886211:0.746227:0.799653:0.746227:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dom: todos los :@0.814889:0.876137:0.881330:0.876137:0.881330:0.866661:0.814889:0.866661:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.881673:0.876752:0.889540:0.876752:0.889540:0.866912:0.881673:0.866912:0.000000
Rec: [–4, + ∞):@0.814894:0.886190:0.871076:0.886190:0.871076:0.876714:0.814894:0.876714:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
V:@0.711226:0.876450:0.716500:0.876450:0.716500:0.867550:0.711226:0.867550:0.000000
(1, –4):@0.716500:0.876450:0.742060:0.876450:0.742060:0.866974:0.716500:0.866974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
V:@0.791891:0.892123:0.797165:0.892123:0.797165:0.883223:0.791891:0.883223:0.000000
1:@0.759498:0.816302:0.764047:0.816302:0.764047:0.808010:0.759498:0.808010:0.000000
–1:@0.754836:0.844632:0.764047:0.844632:0.764047:0.836341:0.754836:0.836341:0.000000:0.000000
–2:@0.754836:0.858801:0.764047:0.858801:0.764047:0.850509:0.754836:0.850509:0.000000:0.000000
–3:@0.754836:0.872969:0.764047:0.872969:0.764047:0.864678:0.754836:0.864678:0.000000:0.000000
–4:@0.754836:0.887138:0.764047:0.887138:0.764047:0.878847:0.754836:0.878847:0.000000:0.000000
2:@0.759498:0.802140:0.764047:0.802140:0.764047:0.793849:0.759498:0.793849:0.000000
3:@0.759498:0.787971:0.764047:0.787971:0.764047:0.779680:0.759498:0.779680:0.000000
4:@0.759498:0.773803:0.764047:0.773803:0.764047:0.765511:0.759498:0.765511:0.000000
5:@0.759498:0.759634:0.764047:0.759634:0.764047:0.751343:0.759498:0.751343:0.000000
–2:@0.726523:0.835963:0.735734:0.835963:0.735734:0.827672:0.726523:0.827672:0.000000:0.000000
–1:@0.745402:0.835963:0.754612:0.835963:0.754612:0.827672:0.745402:0.827672:0.000000:0.000000
1:@0.785480:0.835963:0.790029:0.835963:0.790029:0.827672:0.785480:0.827672:0.000000
2:@0.804358:0.835963:0.808908:0.835963:0.808908:0.827672:0.804358:0.827672:0.000000
3:@0.823237:0.835963:0.827786:0.835963:0.827786:0.827672:0.823237:0.827672:0.000000
4:@0.842115:0.835963:0.846665:0.835963:0.846665:0.827672:0.842115:0.827672:0.000000
5:@0.860994:0.835963:0.865543:0.835963:0.865543:0.827672:0.860994:0.827672:0.000000
–3:@0.707654:0.835963:0.716865:0.835963:0.716865:0.827672:0.707654:0.827672:0.000000:0.000000
–4:@0.688775:0.835963:0.697986:0.835963:0.697986:0.827672:0.688775:0.827672:0.000000:0.000000