// Numbas version: finer_feedback_settings {"name": "Gu\u00eda 3 - NM2 - Funci\u00f3n Cuadr\u00e1tica Pregunta 6", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Screenshot_3_q3CIRwS.jpg", "/srv/numbas/media/question-resources/Screenshot_3_q3CIRwS.jpg"], ["question-resources/Screenshot_4_gNeBmXk.jpg", "/srv/numbas/media/question-resources/Screenshot_4_gNeBmXk.jpg"], ["question-resources/A.jpg", "/srv/numbas/media/question-resources/A.jpg"], ["question-resources/A_MfKRlOH.jpg", "/srv/numbas/media/question-resources/A_MfKRlOH.jpg"], ["question-resources/B.jpg", "/srv/numbas/media/question-resources/B.jpg"], ["question-resources/C.jpg", "/srv/numbas/media/question-resources/C.jpg"], ["question-resources/D.jpg", "/srv/numbas/media/question-resources/D.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Gu\u00eda 3 - NM2 - Funci\u00f3n Cuadr\u00e1tica Pregunta 6", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "
6) Determine para la función cuadrática $f(x)=x^2+6x+8$, los coeficientes $\ud835\udc4e$,$\ud835\udc4f$ \ud835\udc66 $\ud835\udc50$, su concavidad, corte en el eje Y, su eje de simetría, vértice y cortes en el eje X. Por medio de los elementos de la parábola construya la gráfica de $\ud835\udc53$.
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\n$a=$[[0]]
\n$b=$[[1]]
\n$c=$[[2]]
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\nRecordando la siguiente regla:
\nValor de $a$ | \nConvidad | \nAbertura | \n
\n $a>0$ \nPositivo \n | \nHacia arriba | \n\n |
\n $a<0$ \nNegativo \n | \nHacia abajo | \n\n |
Por tanto, en la función $f(x)=x^2+6x+8$, el valor de $a=$[[0]], cuyo valor es [[1]] $0$, por tanto la parábola es [[2]].
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\nPaso 1: Primero debemos determinar los valores de $a$ y $b$ en la función $f(x)=x^2+6x+8$, los cuales son:
\n$a=$[[0]]
\n$b=$[[1]]
\nPaso 2: Reemplazar $a$ y $b$ en la expresión $x=$$\\Large -\\frac{b}{2a}$, obteniendo que el eje de simetría es:
\n[[1]] [[1]]
\n$x=-$___________$=-$__________$=$[[3]]
\n$2 \\cdot$ [[0]] [[2]]
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\nRecordemos que $x$ se obtiene de la expresión $x=$$\\Large -\\frac{b}{2a}$, valor que obtuvimos en el eje de simetría el cual es $x=$[[0]].
\nCoordenada $y$:
\nLa coordenada $y$ se obtiene al evaluar $x=$[[0]] en la función $f(x)=x^2+6x+8$, obteniendo:
\n$y=f($[[0]]$)=($[[0]]$)^2+6 \\cdot$[[0]]$+8$
\n$y=f($[[0]]$)=$[[1]][[2]]$+8$
\n$y=f($[[0]]$)=$[[3]]
\nLuego el vértice tiene por coordenadas $(x,y)=($[[4]]$,$[[5]]$)$.
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\nPaso 1: Debemos pensar en dos números $a$ y $b$ que multiplicados sean igual a $8$ y sumados sean igual a $2$ (considere $a$ mayor que $b$ para obtener la respuesta correcta)
\n$a=$[[0]]
\n$b=$[[1]]
\nPaso 2: De lo anterior obtenemos la factorización y ecuación:
\n$(x+a)\\cdot(x+b)=0$
\n$(x+$ [[2]] $) \\cdot (x+$ [[3]] $)=0$
\nPaso 3: Debemos resolver la ecuaciones de primer grado:
\n$x+$[[2]]$=0$ y $x+$[[3]]$=0$
\n$x_1=$[[4]] y $x_2=$[[5]]
\nPaso 4: Determinar las coordenadas de corte del eje X, las cuales son $(x_1,0)=($[[6]]$,0)$ y $(x_2,0)=($[[7]]$,0)$.
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"exploreObjective": null, "minValue": "-2", "maxValue": "-2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Gr\u00e1fica de la funci\u00f3n", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "De acuerdo a lo anteriormente calculado determine cual de las siguientes gráficas corresponde a la gráfica de $f(x)=x^2+6x+8$.
\n[[0]]
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