// Numbas version: finer_feedback_settings
{"name": "Unit 4 - Which quadratic function is shown by the parabola?", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "parts": [{"showFeedbackIcon": true, "maxMarks": 0, "variableReplacementStrategy": "originalfirst", "displayColumns": 0, "type": "1_n_2", "matrix": "[2,0,0,0,0]", "steps": [{"variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "marks": 0, "prompt": "<p>You can narrow down the choices by checking points where the curve intersects the axes, in particular, the $y$-axis intercept. In addition, the $x$-coordinate of the vertex of the parabola is $x=\\frac{-b}{2a}$, when the curve is written in the standard form $y=ax^2+bx+c$. The line $x=\\frac{-b}{2a}$ is also the vertical line of symmetry for the curve.</p>", "showCorrectAnswer": true, "type": "information"}], "displayType": "radiogroup", "stepsPenalty": "1", "variableReplacements": [], "choices": "[function1,function2,function3,function4,function5]", "scripts": {}, "prompt": "<p>Decide which of the following expressions for $f(x)$ corresponds to the parabola shown.</p>", "marks": 0, "minMarks": 0, "shuffleChoices": true, "showCorrectAnswer": true}], "functions": {"drawgraph": {"parameters": [], "language": "javascript", "type": "html", "definition": "      var miny = Numbas.jme.unwrapValue(scope.variables.miny);\n      var maxy = Numbas.jme.unwrapValue(scope.variables.maxy);\n      var minx = Numbas.jme.unwrapValue(scope.variables.minx);\n      var maxx = Numbas.jme.unwrapValue(scope.variables.maxx);\n      var a_inverse = Numbas.jme.unwrapValue(scope.variables.a_inverse);\n      var b = Numbas.jme.unwrapValue(scope.variables.b);\n      var c = Numbas.jme.unwrapValue(scope.variables.c);\n      \n      var div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',\n      {boundingBox:[minx,maxy,maxx,miny],\n       axis:false,\n       showNavigation:false,\n       grid:true});\n        JXG.Options.text.useMathJax = true;\n        var brd = div.board;          \n        var xaxis=brd.createElement('axis', [[minx,0],[maxx,0]]);\n        var yaxis=brd.createElement('axis', [[0,miny],[0,maxy]]);\n        var xlabel = brd.create('text',[maxx-1,0,function(){return '\\\\[x\\\\]';}]);\n        var ylabel = brd.create('text',[-2,maxy,function(){return '\\\\[y\\\\]';}]);\n        var graph = brd.create('functiongraph',[function(x){ return (1/a_inverse)*x*x+b*x+c;},minx,maxx]);\n\nreturn div;\n      "}}, "tags": [], "preamble": {"css": "", "js": ""}, "ungrouped_variables": [], "variables": {"c": {"definition": "random(-7..7 except [b,0,-1,1])", "name": "c", "templateType": "anything", "description": "", "group": "Graph parameters"}, "function4": {"definition": "\"<p>$\\\\var{a_inverse}\\\\simplify{x^2+{b}}\\\\simplify{x+{c}}$</p>\"", "name": "function4", "templateType": "long string", "description": "", "group": "Graph parameters"}, "function1": {"definition": "\"<p>$\\\\frac{1}{\\\\var{a_inverse}}\\\\simplify{x^2+{b}}\\\\simplify{x+{c}}$</p>\"", "name": "function1", "templateType": "long string", "description": "", "group": "Graph parameters"}, "function3": {"definition": "\"<p>$\\\\var{a_inverse}\\\\simplify{x^2+{b}}\\\\simplify{x-{c}}$</p>\"", "name": "function3", "templateType": "long string", "description": "", "group": "Graph parameters"}, "b": {"definition": "random([-4,-3,-2,2,3,4] except a_inverse)", "name": "b", "templateType": "anything", "description": "", "group": "Graph parameters"}, "maxx": {"definition": "20", "name": "maxx", "templateType": "anything", "description": "", "group": "Graph parameters"}, "maxy": {"definition": "15", "name": "maxy", "templateType": "anything", "description": "", "group": "Graph parameters"}, "minx": {"definition": "-20", "name": "minx", "templateType": "anything", "description": "", "group": "Graph parameters"}, "miny": {"definition": "-15", "name": "miny", "templateType": "anything", "description": "", "group": "Graph parameters"}, "function2": {"definition": "\"<p>$\\\\frac{1}{\\\\var{a_inverse}}\\\\simplify{x^2+{b}*3}\\\\simplify{x+{c}}$</p>\"", "name": "function2", "templateType": "long string", "description": "", "group": "Graph parameters"}, "function5": {"definition": "\"<p>$(\\\\simplify{x+{c}})^2+\\\\simplify{x+{b}}$</p>\"", "name": "function5", "templateType": "long string", "description": "", "group": "Graph parameters"}, "a_inverse": {"definition": "random(2..5)", "name": "a_inverse", "templateType": "anything", "description": "", "group": "Graph parameters"}}, "extensions": ["jsxgraph"], "variable_groups": [{"variables": ["minx", "maxx", "miny", "maxy", "a_inverse", "b", "c", "function1", "function2", "function3", "function4", "function5"], "name": "Graph parameters"}], "advice": "", "name": "Unit 4 - Which quadratic function is shown by the parabola?", "statement": "<p><span style=\"font-weight: 400;\">The curve $y=f(x)$ is shown below.<br/></span></p>\n<table>\n<tbody>\n<tr>\n<td>{drawgraph()}</td>\n</tr>\n</tbody>\n</table>", "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "<p>Tests the ability to match a quadratic function to a given parabola. </p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}]}]}], "contributors": [{"name": "Richard Miles", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/882/"}]}