// Numbas version: exam_results_page_options
{"name": "Sketching functions", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"graph": {"definition": "// set up the board\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-2.5,11,2.5,-11],grid:true,withLabel:true,ticks:false});\n\nvar board = div.board;\n\nvar d = board.create('point',[2.1,0],{size:-1,name:'x'});\nd.setProperty({fixed:true});\nvar f = board.create('point',[0,10],{size:-1,name:'y'});\nf.setProperty({fixed:true});\nvar e = board.create('point',[-2,0],{size:5,name:'A'});\ne.setProperty({fixed:true});\nvar g = board.create('point',[0,0],{size:5,name:'B'});\ng.setProperty({fixed:true});\nvar e = board.create('point',[2,0],{size:5,name:'C'});\ne.setProperty({fixed:true});\n\nboard.create('functiongraph',[function(x){ return a*x*x+b*x+c;},-2,2],{strokeColor:'blue',strokeWidth:2});\n\nreturn div;", "parameters": [["a", "number"], ["b", "number"], ["c", "number"]], "language": "javascript", "type": "html"}}, "preamble": {"css": "table#values th {\n  background: none;\n  text-align: center;\n}", "js": "function dragpoint_board() {\n  var scope = question.scope;\n  \n  var a = scope.variables.a.value;\n  var b = scope.variables.b.value;\n  var c = scope.variables.c.value;\n\n  \n  var div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-2.5,11,2.5,-11],grid:true,withLabel:true});\n  $(question.display.html).find('#dragpoint').append(div);\n\n  var board = div.board;\n  \n// ceeate axis labels\n  \n   var label1 = board.create('point',[2.1,0.2],{name:'X',size:-1});\n   label1.setProperty({fixed:true});\n   var label2 = board.create('point',[0,10.3],{name:'y',size:-1});\n   label2.setProperty({fixed:true});\n  \n    \n    \n  //create draggable points\n\n\n    var line0 = board.create('line',[[-2,0],[-2,4]],{visible: false});\n    var np0 = board.create('glider',[-2,8.5,line0],\n      {\n        name:'A',\n        size:5\n      }\n    );\n\n    var line1 = board.create('line',[[0,0],[0,4]],{visible: false});\n    var np1 = board.create('glider',[-1,8.5,line1],\n      {\n        name:'B',\n        size:5\n      }\n    );\n  \n    var line2 = board.create('line',[[2,0],[2,4]],{visible: false});\n    var np2 = board.create('glider',[0,8.5,line2],\n      {\n        name:'C',\n        size:5,\n      }\n    );\n  \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 = 3;\n  var points = [np0, np1, np2];\n  \n  \n  // this function sets up the i^th point\n  function make_point(i) {\n    \n   var point = points[i];\n    \n    var x=point[0];\n    var y=point[1];\n    \n    // the contents of the input box for this point\n    var xstudentAnswer =  question.parts[0].gaps[i].display.studentAnswer;\n\n    \n    // when the student drags the point, update the gapfill input\n    point.on('drag',function(){\n      var x = Numbas.math.niceNumber(point.X());\n      var y = Numbas.math.niceNumber(point.Y());\n      var diff = y-(a*x*x+b*x+c);\n      xstudentAnswer(diff);\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('line',[np0,np1],{straightFirst:false, straightLast:false, strokeWidth:2,strokeColor:'blue'});\n  var parabool = board.create('line',[np1, np2],{straightFirst:false, straightLast:false, strokeWidth:2,strokeColor:'blue'});\n\n}\n\nquestion.signals.on('HTMLAttached',function() {\n  dragpoint_board();\n}); "}, "parts": [{"showFeedbackIcon": true, "prompt": "<div id=\"dragpoint\"></div>", "marks": 0, "scripts": {}, "gaps": [{"showFeedbackIcon": false, "mustBeReduced": false, "showCorrectAnswer": true, "scripts": {}, "maxValue": "{a}+0.2", "correctAnswerFraction": false, "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "marks": "1", "mustBeReducedPC": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "allowFractions": false, "minValue": "{a}-0.2"}, {"showFeedbackIcon": false, "mustBeReduced": false, "showCorrectAnswer": true, "scripts": {}, "maxValue": "0.2", "correctAnswerFraction": false, "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "marks": "1", "mustBeReducedPC": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "allowFractions": false, "minValue": "-0.2"}, {"showFeedbackIcon": false, "mustBeReduced": false, "showCorrectAnswer": true, "scripts": {}, "maxValue": "0.2", "correctAnswerFraction": false, "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "marks": "1", "mustBeReducedPC": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "allowFractions": false, "minValue": "-0.2"}, {"showFeedbackIcon": false, "mustBeReduced": false, "showCorrectAnswer": true, "scripts": {}, "maxValue": "0.2", "correctAnswerFraction": false, "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "marks": "1", "mustBeReducedPC": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "allowFractions": false, "minValue": "-0.2"}, {"showFeedbackIcon": false, "mustBeReduced": false, "showCorrectAnswer": true, "scripts": {}, "maxValue": "0.2", "correctAnswerFraction": false, "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "marks": "1", "mustBeReducedPC": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "allowFractions": false, "minValue": "-0.2"}], "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "type": "gapfill"}], "variablesTest": {"maxRuns": "200", "condition": "4*a+2*b+c<=10 and 4*a+2*b+c>=-10 and 4*a-2*b+c<=10 and 4*a-2*b+c>=-10 and (-b/(2*a) < -2 or -b/(2*a) >2 or (-(b^2-4*a*c)/(4*a) <= 10 and -(b^2-4*a*c)/(4*a) >= -10))"}, "variable_groups": [], "variables": {"b": {"description": "<p>The function is f(x)=ax^2+bx+c.</p>", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "definition": "random(-5..5 except 0)"}, "a": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "definition": "random(2..5)"}, "c": {"description": "<p>The function is f(x)=ax^2+bx+c.</p>", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "definition": "random(-9..9)"}}, "tags": [], "extensions": ["jsxgraph"], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "advice": "<p>The correct graph is shown below.</p>\n<p>{graph(a,b,c)}</p>", "rulesets": {}, "statement": "<p style=\"text-align: center;\"></p>\n<p>By dragging the points A, B, and C, construct the graph of the function</p>\n<p>$ f(x) = \\left\\{ \\begin{array}{cl} \\var{a}&nbsp;\\\\ \\simplify{{b}x + {a}}.\\end{array}\\right.$</p>\n<p>Note that in order to be marked correct, the points need to be within 0.2 of their correct $y$-values.</p>\n<p>Also note that you have to drag each of the points in order to be able to submit your answer.</p>", "ungrouped_variables": ["a", "b", "c"], "name": "Sketching functions", "type": "question", "contributors": [{"name": "Gareth Woods", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/978/"}]}]}], "contributors": [{"name": "Gareth Woods", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/978/"}]}