// Numbas version: exam_results_page_options {"name": "Sin graph wavelength and amplitude", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"eqnline": {"definition": "// This function creates the board and sets it up, then returns an\n// HTML div tag containing the board.\n \n// The line is described by the equation \n// y = a*x + b\n\n// This function takes as its parameters the coefficients a and b,\n// and the coordinates (x2,y2) of a point on the line.\n\n// First, make the JSXGraph board.\n// The function provided by the JSXGraph extension wraps the board up in \n// a div tag so that it's easier to embed in the page.\nvar div = Numbas.extensions.jsxgraph.makeBoard('600px','600px',\n{boundingBox: [-6,3,6,-3],\n axis: false,\n showNavigation: true,\n //grid: true\n grid: true\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.\nvar xaxis = board.create('line',[[0,0],[1,0]], { strokeColor: 'black', fixed: true});\n//var xticks = board.create('ticks',[xaxis,60],{\nvar xticks = board.create('ticks',[xaxis,2],{\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 });\nvar yticks = board.create('ticks',[yaxis,1],{\ndrawLabels: true,\nlabel: {offset: [-20, 0]},\nminorTicks: 0\n});\n\n// mark the two given points - one on the y-axis, and one at (x2,y2)\n\n\n\n\n//board.create('functiongraph',[function(x){ return (x-a)*(x-b);},-8,8]);\n//board.create('functiongraph',[function(x){ return (x-a)*(x-b)+v;},-8,8],{ strokeColor: 'red'});\n\n//board.create('functiongraph',[function(x){ return Math.sin(x*(Math.PI/180));},-360,360]);\n//board.create('functiongraph',[function(x){ return Math.sin((x-60*v)*(Math.PI/180));},-360,360],{ strokeColor: 'red'});\n//board.create('functiongraph',[function(x){ return Math.sin((x+60*v)*(Math.PI/180));},-360,360],{ strokeColor: 'black'});\nboard.create('functiongraph',[function(x){ return Math.sin(x);},-7,7],{ strokeColor: 'red'});\nreturn div;", "type": "html", "language": "javascript", "parameters": [["a", "number"], ["b", "number"], ["x2", "number"], ["y2", "number"], ["v", "number"]]}}, "ungrouped_variables": ["a", "x2", "b", "y2", "c", "v", "degrees"], "name": "Sin graph wavelength and amplitude", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "

We know that the graph crosses the \$x\$-axis at both \$(\\var{a},0)\$ and \$(\\var{b},0)\$. Since this is a quadratic, we know our equations has two roots, and by the previous observation, they are at \$\\var{a}\$ and \$\\var{b}\$. Hence we can write our equation as \$\\simplify{y=(x-{a})(x-{b})}\$ which simplifies to \$\\simplify{y=x^2-({a}+{b})x+({a}*{b})}\$.

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To find the coefficients of the turning point of the quadratic, we know the x-coordinate of the turning point will correspond to the solution to \$dy/dx=0\$. So we get \$\\simplify{2x-({a}+{b})}=0\$ hence \$\\simplify{x=({a}+{b})/2}\$. We substitute this value of x back into the equation of the quadratic to find the corresponding y-coordinate.

", "rulesets": {}, "parts": [{"prompt": "

The Blue graph has been transformed onto the red graph \$g(x)\$, type in the equation of the line red line.

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\$g(x)=\\;\$[[0]]

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{eqnline(a,b,x2,y2,v)}

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The Blue graph shows a graph of a quadratic equation, \$f(x)=sin(x)\$

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(-4..4 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "a*b", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(-5..5 except [0,a,-a])", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "degrees": {"definition": "60*v", "templateType": "anything", "group": "Ungrouped variables", "name": "degrees", "description": ""}, "v": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "v", "description": ""}, "x2": {"definition": "random(-3..3 except -1..1)", "templateType": "anything", "group": "Ungrouped variables", "name": "x2", "description": ""}, "y2": {"definition": "x2*a+b", "templateType": "anything", "group": "Ungrouped variables", "name": "y2", "description": ""}}, "metadata": {"description": "

Given th original formula the student enters the transformed formula

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