This is a calculator question.
", "name": "Differentiation: Equation of tangent. Quadratic", "variables": {"fx": {"templateType": "anything", "group": "part a", "description": "", "definition": "a*x*x+b*x+c", "name": "fx"}, "fx0": {"templateType": "anything", "group": "part a", "description": "", "definition": "a*x0*x0+b*x0+c", "name": "fx0"}, "c": {"templateType": "anything", "group": "part a", "description": "", "definition": "random(-2..2 except 0)", "name": "c"}, "m": {"templateType": "anything", "group": "part a", "description": "", "definition": "2*a*x+b", "name": "m"}, "b": {"templateType": "anything", "group": "part a", "description": "", "definition": "random(-5..5 except 0)", "name": "b"}, "a": {"templateType": "anything", "group": "part a", "description": "", "definition": "random(-2..2 except 0)", "name": "a"}, "absfx": {"templateType": "anything", "group": "part a", "description": "", "definition": "abs(fx)", "name": "absfx"}, "x0": {"templateType": "anything", "group": "part a", "description": "", "definition": "-b/(2a)", "name": "x0"}, "x": {"templateType": "anything", "group": "part a", "description": "", "definition": "random(-3..3 except 0)", "name": "x"}}, "variable_groups": [{"name": "part a", "variables": ["a", "b", "c", "x", "fx", "m", "absfx", "x0", "fx0"]}], "extensions": ["jsxgraph"], "variablesTest": {"condition": "and(m<>0,(absfx<15))", "maxRuns": 100}, "functions": {"plot": {"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;", "parameters": [["a", "number"], ["b", "number"], ["c", "number"], ["x0", "number"], ["y0", "number"]], "language": "javascript", "type": "html"}}, "ungrouped_variables": [], "preamble": {"js": "", "css": ""}, "advice": "See Lecture 9.4 and Workshop 9.5 for the background and examples.
\nIf you're unsure on equation of straight lines, go to Week 4 of Maths 1. Look at the lectures, workshops and/or CLEs.
\n\n(a) Similar questions are in Lecture 9.4 and Workshop 9.5.
\n\n(b) There is not an example like (b) in the lectures or workshops. You will have to think for yourself. Some hints:
\n-- What does the information provided tell us about the gradient of the line.
\n-- Once you know the gradient of the line, you have to find the appropriate value of $x$ which achieves this gradient.
", "parts": [{"scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "marks": 0, "gaps": [{"scripts": {}, "checkVariableNames": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "type": "jme", "variableReplacementStrategy": "originalfirst", "expectedVariableNames": [], "vsetRangePoints": 5, "marks": "5", "failureRate": 1, "checkingAccuracy": 0.001, "answer": "x*{m}+{fx-x*m}", "showPreview": true, "showCorrectAnswer": true, "checkingType": "absdiff", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "vsetRange": [0, 1], "unitTests": []}, {"scripts": {}, "markPerCell": false, "numRows": 1, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "type": "matrix", "variableReplacementStrategy": "originalfirst", "allowResize": false, "numColumns": "2", "correctAnswerFractions": false, "tolerance": 0, "allowFractions": true, "marks": "3", "correctAnswer": "matrix([x0,fx0])", "showCorrectAnswer": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "unitTests": []}], "sortAnswers": false, "showCorrectAnswer": true, "prompt": "The curve with equation $y = \\simplify{{a}x^2+{b}x+{c}}$ is sketched below.
\n{plot(a,b,c,x, fx)}
\nIn addition, the tangent to the curve at $x=\\var{x}$ has been drawn.
\n(a) What is the equation of the tangent? $y= $ [[0]]
\n\n(b) $L$ is a horizontal straight line which is tangent to the curve. Determine the coordinates of where the line $L$ touches the curve.
\n[[1]]
\n", "customMarkingAlgorithm": "", "unitTests": []}], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "A quadratic is and a graph of it is given. A tangent is also sketch. The equation of the tangent line is asked for.
"}, "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/"}]}