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{"name": "BASIS: 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": "BASIS: Vind constante c voor kwadratische functie (gegeven a en b)", "tags": [], "metadata": {"description": "<p>1) Voer de vraag zelf uit als leerling</p>\n<p>2) Randomiseer deze vraag. Vervang de concrete getalletjes door willekeurig getrokken variabelen, maar zorg dat de vraagstelling en modeloplossing nog mooi eruit zien.</p>\n<p>3) Controleer of de willekeurige getallen altijd even moeilijk zijn, of de randomisatie soms significant moeilijker is. Indien ze moeilijker is, beperk die gevallen bij Variable Testing.</p>", "licence": "None specified"}, "statement": "<p>The function $f: y=2x^2+2x+c$ has $0$ 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 $x=-\\frac{b}{2a}=-\\frac{2}{4}=-\\frac{1}{2}$.</p>\n<p>The extremal value itself is&nbsp; given by $f(-\\frac{1}{2})=-\\frac{1}{2}+c$.&nbsp; Since this must be equal to $0$, we find $-\\frac{1}{2}+c=0$, hence $c=\\frac{1}{2}$.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "prompt": "<p>Find $c$.</p>", "minValue": "0.5", "maxValue": "0.5", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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/"}]}