// Numbas version: exam_results_page_options
{"name": "VOORBEELDOPLOSSING: Vind constante c voor kwadratische functie (gegeven a en b)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "VOORBEELDOPLOSSING: Vind constante c voor kwadratische functie (gegeven a en b)", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>The function $f: y=\\simplify{{a}*x^2+{b}*x+c}$ has $\\var{yv}$ as an extreme value.</p>", "advice": "<p>A quadratic function $f:y=ax^2+bx+c$ has a parabolic graph and reaches it extremal value at the vertex.</p>\n<p>The $x$-value of the vertex is found as $x=-\\frac{b}{2a}=\\simplify{{-b}/{2*a}}=\\var{xv}$.</p>\n<p>The extremal value itself is&nbsp; given by $f(\\var{xv})=\\var{yv-c}+c$.&nbsp; Since this must be equal to $\\var{yv}$, we find $\\var{yv-c}+c=\\var{yv}$, hence $c=\\var{c}$.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"yv": {"name": "yv", "group": "Ungrouped variables", "definition": "random(-4 .. 4#0.2)", "description": "<p>y-coordinate of the vertex</p>", "templateType": "randrange", "can_override": true}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-5..5)", "description": "<p>co&euml;ffici&euml;nt van kwadratische term van kwadratische functie</p>", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "-2*xv*a", "description": "<p>coefficient van lineare term van kwadratische functie</p>", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "yv+a*xv^2", "description": "<p>constante term van kwadratische functie</p>", "templateType": "anything", "can_override": false}, "xv": {"name": "xv", "group": "Ungrouped variables", "definition": "random(-5 .. 5#1)", "description": "<p>x-coordinate of the vertex</p>", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "a<>0", "maxRuns": 100}, "ungrouped_variables": ["xv", "yv", "a", "b", "c"], "variable_groups": [], "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>Find $c$.</p>\n<p>$c=$[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{c}", "maxValue": "{c}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Eric Boeckx", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3901/"}, {"name": "Alexander Holvoet", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/19859/"}]}]}], "contributors": [{"name": "Eric Boeckx", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3901/"}, {"name": "Alexander Holvoet", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/19859/"}]}