// Numbas version: exam_results_page_options
{"name": "Quadratic functions: Interpreting Graphs - Fitness of Population", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Quadratic functions: Interpreting Graphs - Fitness of Population", "tags": [], "metadata": {"description": "<p>The question includes a quadratic graph depicting the relationship between the frequency&nbsp;of an allele A at a genetic locus in a diploid population and the fitness of a population with this frequency of allele A. The aim is to estimate the maximum and minimum fitness of the population and the corresponding frequency of allele A.</p>", "licence": "None specified"}, "statement": "<p>The following graph depicts the relationship between the frequency, $x$, of an allele A at a genetic locus in a diploid population and the fitness, $w$, of a population with this frequency of allele A.</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/rtngjns4', defs)}</p>", "advice": "<p>{geogebra_applet('https://www.geogebra.org/m/xw4jjqxa',defsad1)}</p>\n<p>Note: you can zoom in and out of the figure as needed.</p>\n<p>a) We first need to locate the highest point on the graph. From that point, we can draw a line perpendicular to the vertical axis to estimate the maximum fitness and a line perpendicular to the horizontal axis to estimate the corresponding frequency of allele A.&nbsp;</p>\n<p>Here, a good estimate could be:</p>\n<ul>\n<li>maximum fitness, $w_{max}=\\var{max}$</li>\n<li>frequency of allele A, $x=\\var{xmax}$.</li>\n</ul>\n<p>b)We first need to locate the lowest point on the graph. From that point, we can draw a line perpendicular to the vertical axis to estimate the minimum fitness and a line perpendicular to the horizontal axis to estimate the corresponding frequency of allele A.&nbsp;</p>\n<p>Here, a good estimate could be:</p>\n<ul>\n<li>minimum fitness, $w_{min}=\\var{min}$</li>\n<li>frequency of allele A, $x=\\var{xmin}$.</li>\n</ul>", "rulesets": {}, "extensions": ["geogebra"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "problem posing variables", "definition": "random (0 .. 0.5 # 0.1 except 0)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "problem posing variables", "definition": "random([1,2])", "description": "", "templateType": "anything", "can_override": false}, "x_1": {"name": "x_1", "group": "problem posing variables", "definition": "random (0..1 #0.05 except [0,1]) ", "description": "", "templateType": "anything", 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"", "templateType": "anything", "can_override": false}, "turn": {"name": "turn", "group": "answer variables", "definition": "-coef_b/(2*coef_a)", "description": "", "templateType": "anything", "can_override": false}, "max": {"name": "max", "group": "answer variables", "definition": "if(turn<1, max([{coef_c},{coef_a}+{coef_b}+{coef_c}, {coef_a}*{turn}^2+{coef_b}*{turn}+{coef_c}]), max({coef_c},{coef_a}+{coef_b}+{coef_c))", "description": "", "templateType": "anything", "can_override": false}, "min": {"name": "min", "group": "answer variables", "definition": "if(turn<1, min([{coef_c},{coef_a}+{coef_b}+{coef_c}, {coef_a}*{turn}^2+{coef_b}*{turn}+{coef_c}]), min({coef_c},{coef_a}+{coef_b}+{coef_c))", "description": "", "templateType": "anything", "can_override": false}, "xmax": {"name": "xmax", "group": "answer variables", "definition": "if(max=coef_c,0,if(max=coef_a+coef_b+coef_c,1,turn))", "description": "", "templateType": "anything", "can_override": false}, "xmin": {"name": "xmin", "group": "answer variables", "definition": "if(min=coef_c,0,if(min=coef_a+coef_b+coef_c,1,turn))", "description": "", "templateType": "anything", "can_override": false}, "Maxpoint": {"name": "Maxpoint", "group": "Ungrouped variables", "definition": "vector(xmax,max)", "description": "", "templateType": "anything", "can_override": false}, "MinPoint": {"name": "MinPoint", "group": "Ungrouped variables", "definition": "vector(xmin,min)", "description": "", "templateType": "anything", "can_override": false}, "defsad1": {"name": "defsad1", "group": "Ungrouped variables", "definition": "[\n  ['a',coef_a],\n  ['b',coef_b],\n  ['c',coef_c],\n  ['A',maxpoint],\n  ['B',minpoint]\n  ]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "(coef_a<0)", "maxRuns": 100}, "ungrouped_variables": ["defs", "Maxpoint", "MinPoint", "defsad1"], "variable_groups": [{"name": "problem posing variables", "variables": ["a", "b", "x_1", "w_1", "c"]}, {"name": "answer variables", "variables": ["coef_a", "coef_b", "coef_c", "turn", "max", "min", "xmax", "xmin"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Use the graph to find the maximum possible fitness and the value of $x$ at which this maximum is attained.</p>\n<ul>\n<li>Maximum fitness, $w_{max}=$ [[0]].</li>\n<li>Frequency of allele A, $x=$ [[1]].</li>\n</ul>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, 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