// Numbas version: finer_feedback_settings
{"name": "Gu\u00eda 3 - NM2 - Funci\u00f3n Cuadr\u00e1tica Pregunta 5", "extensions": [], "custom_part_types": [], "resources": [], "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 5", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>5)&nbsp; Determine las coordenadas de los puntos de corte del <strong>eje X</strong> de la funci&oacute;n $f(x)=x^2+7x+12$.</p>\n<p>&nbsp; &nbsp; &nbsp;A)&nbsp; &nbsp; $(-4,0)$&nbsp; y&nbsp; $(3,0)$</p>\n<p>&nbsp; &nbsp; &nbsp;B)&nbsp; &nbsp;&nbsp;$(4,0)$&nbsp; y&nbsp; $(3,0)$</p>\n<p>&nbsp; &nbsp; &nbsp;C)&nbsp; &nbsp;&nbsp;$(-4,0)$&nbsp; y&nbsp; $(-3,0)$</p>\n<p>&nbsp; &nbsp; &nbsp;D)&nbsp; &nbsp;&nbsp;$(4,0)$&nbsp; y&nbsp; $(-3,0)$</p>", "advice": "", "rulesets": {}, "extensions": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Desarrollo", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Para determinar los puntos de corte en el <strong>eje X</strong> debemos resolver la ecuaci&oacute;n de segundo grado&nbsp;$f(x)=x^2+7x+12=0$, para ello realizaremos los siguientes pasos:</p>\n<p><strong>Paso 1:&nbsp;</strong>En la ecuaci&oacute;n&nbsp;$f(x)=x^2+7x+12=0$, debemos primero pensar en dos n&uacute;meros $a$ y $b$ que cumplan las siguientes condiciones, que multiplicados sean igual a 12 y sumados sean igual a 7, estos dos n&uacute;meros son $a=$[[0]]&nbsp; y&nbsp; $b=$[[1]].&nbsp;<strong>(Observaci&oacute;n aqu&iacute; $a&gt;b$)</strong></p>\n<p><strong>Paso 2: </strong>Con los valores&nbsp;$a=$[[0]]&nbsp; y&nbsp; $b=$[[1]], obtenemos la siguiente factorizaci&oacute;n:</p>\n<p>$(x+a) \\cdot (x+b)=0$=$(x+$[[2]]$)\\cdot(x+$[[3]]$)=0$</p>\n<p><strong>Paso 3:&nbsp;</strong>Determinamos de la factorizaci&oacute;n las ecuaciones:</p>\n<p>$x+a=0$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; $x+b=0$</p>\n<p>$x+$[[4]]$=0$&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;$x+$[[5]]$=0$</p>\n<p><strong>Paso 4: </strong>Despejamos las ecuaciones del <strong>paso 3</strong>, obteniendo que las <strong>coodenadas</strong>&nbsp;<strong>x&nbsp;</strong>de los puntos de corte del <strong>eje X</strong> son:</p>\n<p>$x_1=$[[6]]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; $x_2=$[[7]]</p>\n<p><strong>Paso 5:&nbsp;</strong>Las coordenadas de corte son $(x_1,0)=($[[8]]&nbsp;$,0)$&nbsp; y&nbsp; &nbsp;$(x_2,0)=($[[9]]&nbsp;$,0)$</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "4", "maxValue": "4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.1", "scripts": {}, 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