// Numbas version: exam_results_page_options
{"name": "Graph of a quadratic function", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Graph of a quadratic function", "tags": ["JSXgraph", "jsxgraph", "Jsxgraph", "plot", "quadratic"], "metadata": {"description": "<p>Compute a table of values for a quadratic function. A JSXgraph plot shows the curve going through the entered values.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>You are given the quadratic formula</p>\n<p>$y=\\simplify[std]{{a}x^2+{c}}$</p>", "advice": "", "rulesets": {"std": ["all", "fractionNumbers"]}, "extensions": ["jsxgraph"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-2,-1,-0.5,0.5,1,2)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-4..4 except 0)", "description": "", "templateType": "anything", "can_override": false}, "ys": {"name": "ys", "group": "Ungrouped variables", "definition": "map(a*x^2+c,x,-3..3)", "description": "<p>The $y$-coordinates of the points to plot.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "c", "ys"], "variable_groups": [], "functions": {}, "preamble": {"js": "function dragpoint_board() {\n  var scope = question.scope;\n  \n  var a = scope.variables.a.value;\n  var c = scope.variables.c.value;\n  var maxy = Math.max(Math.abs(a*9+c),Math.abs(c));\n  \n  var div = Numbas.extensions.jsxgraph.makeBoard('250px','400px',{boundingBox:[-5,maxy+3,5,-maxy-3],grid:true});\n  $(question.display.html).find('#dragpoint').append(div);\n  \n  var board = div.board;\n  \n  //shorthand to evaluate a mathematical expression to a number\n  function evaluate(expression) {\n    try {\n      var val = Numbas.jme.evaluate(expression,question.scope);\n      return Numbas.jme.unwrapValue(val);\n    }\n    catch(e) {\n      // if there's an error, return no number\n      return NaN;\n    }\n  }\n  \n  // set up points array\n  var num_points = 7;\n  var points = [];\n  \n  \n  // this function sets up the i^th point\n  function make_point(i) {\n    \n    // calculate initial coordinates\n    var x = i-(num_points-1)/2;\n    \n    // create an invisible vertical line for the point to slide along\n    var line = board.create('line',[[x,0],[x,1]],{visible: false});\n    \n    // create the point\n    var point = points[i] = board.create(\n      'glider',\n      [i-(num_points-1)/2,0,line],\n      {\n        name:'',\n        size:2,\n        snapSizeY: 0.1,  // the point will snap to y-coordinates which are multiples of 0.1\n        snapToGrid: true\n      }\n    );\n    \n    // the contents of the input box for this point\n    var studentAnswer = question.parts[1].gaps[i].display.studentAnswer;\n    \n    // watch the student's input and reposition the point when it changes.    \n    ko.computed(function() {\n      y = evaluate(studentAnswer());\n      if(!(isNaN(y)) && board.mode!=board.BOARD_MODE_DRAG) {\n        point.moveTo([x,y],100);\n      }\n    });\n    \n    // when the student drags the point, update the gapfill input\n    point.on('drag',function(){\n      var y = Numbas.math.niceNumber(point.Y());\n      studentAnswer(y);\n    });\n    \n  }\n  \n  // create each point\n  for(var i=0;i<num_points;i++) {\n    make_point(i);\n  }\n  \n  // create the parabola\n  var parabool = board.create('spline',points,{strokeWidth:3,strokeColor:'red'});\n}\n\nquestion.signals.on('HTMLAttached',function() {\n  dragpoint_board();\n}); ", "css": "table#values th {\n  background: none;\n  text-align: center;\n}"}, "parts": [{"type": "1_n_2", "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>The graph of this formula is:</p>", "minMarks": 0, "maxMarks": 1, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>An upwards-opening parabola</p>", "<p>A downwards-opening parabola</p>"], "matrix": ["if(a>0,1,0)", "if(a>0,0,1)"], "distractors": ["", ""]}, {"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>Fill in the table of values for $y=\\simplify[std]{{a}x^2+{c}}$:</p>\n<table id=\"values\">\n<thead>\n<tr><th>$x$</th><th>$-3$</th><th>$-2$</th><th>$-1$</th><th>$0$</th><th>$1$</th><th>$2$</th><th>$3$</th></tr>\n</thead>\n<tbody>\n<tr><th>$y$</th>\n<td>[[0]]</td>\n<td>[[1]]</td>\n<td>[[2]]</td>\n<td>[[3]]</td>\n<td>[[4]]</td>\n<td>[[5]]</td>\n<td>[[6]]</td>\n</tr>\n</tbody>\n</table>\n<div id=\"dragpoint\"></div>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "$x=-3$", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ys[0]", "maxValue": "ys[0]", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "$x=-2$", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ys[1]", "maxValue": "ys[1]", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "$x=-1$", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ys[2]", "maxValue": "ys[2]", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "$x=0$", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ys[3]", "maxValue": "ys[3]", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": 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"adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ys[5]", "maxValue": "ys[5]", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "$x=3$", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ys[6]", "maxValue": "ys[6]", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "matrix", 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