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{"name": "Differentiation: Equation of tangent to Quadratic", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Differentiation: Equation of tangent to Quadratic", "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><strong>Tangent to a Curve</strong></p>", "advice": "", "rulesets": {}, "extensions": ["jsxgraph"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"absfx": {"name": "absfx", "group": "part a", "definition": "abs(fx)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "part a", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything", "can_override": false}, "fx0": {"name": "fx0", "group": "part a", "definition": "a*x0*x0+b*x0+c", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "part a", "definition": "2*a*x+b", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "part a", "definition": "random(-3..3 except 0)", "description": "", "templateType": "anything", "can_override": false}, "fx": {"name": "fx", "group": "part a", "definition": "a*x*x+b*x+c", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "part a", "definition": "random(-2..2 except 0)", "description": "", "templateType": "anything", "can_override": false}, "x0": {"name": "x0", "group": "part a", "definition": "-b/(2a)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "part a", "definition": "random(-2..2 except 0)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "and(m<>0,(absfx<15))", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "part a", "variables": ["a", "b", "c", "x", "fx", "m", "absfx", "x0", "fx0"]}], "functions": {"plot": {"parameters": [["a", "number"], ["b", "number"], ["c", "number"], ["x0", "number"], ["y0", "number"]], "type": "html", "language": "javascript", "definition": "// This functions plots a cubic with a certain number of\n// stationary points and roots.\n// It creates the board, sets it up, then returns an\n// HTML div tag containing the board.\n\n\n// Max and min x and y values for the axis.\nvar x_min = -7;\nvar x_max = 7;\nvar y_min = -20;\nvar y_max = 20;\n\n\n// First, make the JSXGraph board.\nvar div = Numbas.extensions.jsxgraph.makeBoard(\n  '500px',\n  '600px',\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});\nvar 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 a*x*x+b*x+c},x_min,x_max],\n                {strokeWidth:2});\n\n//Plot the tangent.\n    board.create('functiongraph',\n             [function(x){ return y0+(x-x0)*(2*x0*a+b)},x_min,x_max]);\n\n// Plot coordinates.\n    board.create('circle',[[x0,y0],0.1],{color:'red'});\n\n\nreturn div;"}}, "preamble": {"js": "", "css": ""}, "parts": [{"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>A quadratic curve has equation $y = \\simplify{{a}x^2+{b}x+{c}}$.</p>\n<p></p>\n<p><strong>(a)</strong>&nbsp; What is the equation the tangent to the curve at $x=\\var{x}$ ?</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp;The equation of the tangent is required in&nbsp; \\(y=mx+c\\)&nbsp; &nbsp;form.</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp;$y= $&nbsp; [[0]]</p>\n<p></p>\n<p><strong>(b)&nbsp;</strong> Find the coordinates of the point at which the tangent to the curve is horizontal.</p>\n<p>&nbsp; &nbsp; &nbsp; \\((x,y) =\\)</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [[1]]&nbsp;</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "x*{m}+{fx-x*m}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "matrix", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "matrix", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "correctAnswer": "matrix([x0,fx0])", "correctAnswerFractions": false, "numRows": 1, "numColumns": "2", "allowResize": false, "tolerance": 0, "markPerCell": false, "allowFractions": true, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0, "prefilledCells": ""}, {"type": "matrix", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "correctAnswer": "matrix([x0,fx0])", "correctAnswerFractions": true, "numRows": 1, "numColumns": "2", "allowResize": false, "tolerance": 0, "markPerCell": true, "allowFractions": true, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0, "prefilledCells": ""}], "correctAnswer": "matrix([x0,fx0])", "correctAnswerFractions": true, "numRows": 1, "numColumns": "2", "allowResize": false, "tolerance": 0, "markPerCell": true, "allowFractions": true, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0, "prefilledCells": ""}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Clare Lundon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/492/"}, {"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}]}], "contributors": [{"name": "Clare Lundon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/492/"}, {"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}