// Numbas version: exam_results_page_options
{"name": "Algebra: number of solutions of quadratic based on graph", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "advice": "<p>You should be using the graphs to answer this question - there is no need to do any calculations or algebraic things.</p>\n<p>See 4.1 for background on quadratics and see 1.1 for what the word solution means.&nbsp;&nbsp;</p>", "name": "Algebra: number of solutions of quadratic based on graph", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>A quadratic is given and sketched. Based on the sketch, task is to determine the number of solutions to the equation $f(x)=0$.</p>"}, "extensions": ["jsxgraph"], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"js": "", "css": ""}, "ungrouped_variables": [], "statement": "<p>This is a non-calculator question.</p>", "variables": {"a": {"templateType": "anything", "group": "part a", "name": "a", "definition": "shuffle([1,1,1,-1,-1,-1])", "description": ""}, "c": {"templateType": "anything", "group": "part a", "name": "c", "definition": "[a[0]*(answer[0]-1)*-1*random(2..4),\n  a[1]*(answer[1]-1)*-1*random(2..4),\n  a[2]*(answer[2]-1)*-1*random(2..4),\n  a[3]*(answer[3]-1)*-1*random(2..4),\n  a[4]*(answer[4]-1)*-1*random(2..4),\n  a[5]*(answer[5]-1)*-1*random(2..4)\n]", "description": ""}, "b": {"templateType": "anything", "group": "part a", "name": "b", "definition": "shuffle([-4,-2,-1,0,3,4])", "description": ""}, "answer": {"templateType": "anything", "group": "part a", "name": "answer", "definition": "shuffle([1,1,2,2,0,0])", "description": ""}}, "parts": [{"correctAnswerStyle": "plain", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "unitTests": [], "maxValue": "answer[0]", "allowFractions": false, "prompt": "<p>Below is a graph of a quadratic function $y=\\simplify{{a[0]}*x^2 + {-2*a[0]*b[0]}*x + {a[0]*b[0]*b[0]+c[0]}}$.</p>\n<p>{plot(0,a[0],b[0],c[0])}</p>\n<p>How many solutions does the equation $\\simplify{{a[0]}*x^2 + {-2*a[0]*b[0]}*x + {a[0]*b[0]*b[0]+c[0]}}=0$ have?</p>", "correctAnswerFraction": false, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "minValue": "answer[0]", "type": "numberentry", "marks": "0.5", "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true}, {"correctAnswerStyle": "plain", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "unitTests": [], "maxValue": "answer[1]", "allowFractions": false, "prompt": "<p>Below is a graph of a quadratic function $y=\\simplify{{a[1]}*x^2 + {-2*a[1]*b[1]}*x + {a[1]*b[1]*b[1]+c[1]}}$.</p>\n<p>{plot(0,a[1],b[1],c[1])}</p>\n<p>How many solutions does the equation $\\simplify{{a[1]}*x^2 + {-2*a[1]*b[1]}*x + {a[1]*b[1]*b[1]+c[1]}}=0$ have?</p>", "correctAnswerFraction": false, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "minValue": "answer[1]", "type": "numberentry", "marks": "0.5", "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true}, {"correctAnswerStyle": "plain", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "unitTests": [], "maxValue": "answer[2]", "allowFractions": false, "prompt": "<p>Below is a graph of a quadratic function $y=\\simplify{{a[2]}*x^2 + {-2*a[2]*b[2]}*x + {a[2]*b[2]*b[2]+c[2]}}$.</p>\n<p>{plot(0,a[2],b[2],c[2])}</p>\n<p>How many solutions does the equation $\\simplify{{a[2]}*x^2 + {-2*a[2]*b[2]}*x + {a[2]*b[2]*b[2]+c[2]}}=0$ have?</p>", "correctAnswerFraction": false, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "minValue": "answer[2]", "type": "numberentry", "marks": "0.5", "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true}, {"correctAnswerStyle": "plain", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "unitTests": [], "maxValue": "answer[3]", "allowFractions": false, "prompt": "<p>Below is a graph of a quadratic function $y=\\simplify{{a[3]}*x^2 + {-2*a[3]*b[3]}*x + {a[3]*b[3]*b[3]+c[3]}}$.</p>\n<p>{plot(0,a[3],b[3],c[3])}</p>\n<p>How many solutions does the equation $\\simplify{{a[3]}*x^2 + {-2*a[3]*b[3]}*x + {a[3]*b[3]*b[3]+c[3]}}=0$ have?</p>", "correctAnswerFraction": false, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "minValue": "answer[3]", "type": "numberentry", "marks": "0.5", "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true}], "functions": {"plot": {"language": "javascript", "parameters": [["n", "number"], ["a", "number"], ["b", "number"], ["c", "number"]], "definition": "// This functions plots a quadratic of the form a*(x-b)*(x-b)+c\n\n\n// Max and min x and y values for the axis.\nvar x_min = -10;\nvar x_max = 10;\nvar y_min = -10;\nvar y_max = 10;\n\n\n// First, make the JSXGraph board.\nvar div = Numbas.extensions.jsxgraph.makeBoard(\n  '400px',\n  '400px',\n {\n   boundingBox: [x_min,y_max,x_max,y_min],\n   axis: false,\n   showNavigation: false,\n   grid: false,\n   axis:false,\n }\n);\n\n\n\n// div.board is the object created by JSXGraph, which you use to \n// manipulate elements\nvar board = div.board; \n\n// create the x-axis and y-axis\nvar xaxis = board.create('line',[[0,0],[1,0]], { strokeColor: 'black', fixed: true});\n//var xticks = board.create('ticks',[xaxis,1],{\n//  drawLabels: true,\n//  label: {offset: [-4, -10]},\n//  minorTicks: 0\n//});\n\n// create the y-axis\nvar yaxis = board.create('line',[[0,0],[0,1]], { strokeColor: 'black', fixed: true });\n\n\n\n\n// Plot the function.\n//    board.create('functiongraph',\n//             [function(x){ return (x-a)*(x-a)+b},x_min,x_max]);\n\n//Define function depending on value of n.\nswitch(n) {\n    case 0:\n    var f = function(x) {return a*(x-b)*(x-b)+c;    }\n        break;\n    \n//    case 1:\n//    var f = function(x) {return Math.log(x+a); }\n//        break;\n    \n//    case 2:\n//    var f = function(x) {return a*x+b;}\n//        break;\n    \n//    case 3:\n//    var f = function(x) {return Math.pow(2,x)*-a;}\n//        break;\n    \n//    case 4:\n//    var f = function(x) {return a*x*(x-b)*(x-c);}\n//    break;\n    \n}\n\n    board.create('functiongraph', [f], {strokeWidth:2,strokeColor:'black'});\n\nreturn div;\n\n\n\n// Plot coordinates.\n//    board.create('circle',[[x0,y0],0.1],{color:'red'});\n//    board.create('text',[x0,y0+0.3,'A']);\n//    board.create('circle',[[x1,y1],0.1],{color:'red'});\n//    board.create('text',[x1,y1+0.3,'B']);\n//    board.create('circle',[[x2,y2],0.1],{color:'red'});\n//    board.create('text',[x2,y2+0.3,'C']);\n\nreturn div;", "type": "html"}}, "variable_groups": [{"name": "part a", "variables": ["a", "b", "c", "answer"]}], "rulesets": {}, "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}