// Numbas version: exam_results_page_options {"name": "Graph transforms TEST 2", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": 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: [-8,12,8,-12],\n axis: false,\n showNavigation: 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});\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,2],{\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\nboard.create('functiongraph',[function(x){ return (x-a)*(x-a)-b;},-8,8]);\nboard.create('functiongraph',[function(x){ return (x-a+v)*(x-a+v)-b+v+1;},-8,8],{ strokeColor: 'red'});\n\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"], "name": "Graph transforms TEST 2", "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": "

Write the equation of the line in the diagram.

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

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Find the coordinates of the turning point of this quadratic

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\$x=\$[[0]]

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\$y=\$[[1]]

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

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The Blue graph shows a graph of a quadratic equation, \$\\simplify { f(x)=(x-{a})^2-{b}}\$

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The Blue graph has been transformed onto the red graph \$g(x)\$, type in the new function definition:

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\$a=\\var{a}\$

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\$b=\\var{b}\$

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\$c=\\var{c}\$

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\$x2=\\var{x2}\$

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\$y2=\\var{y2}\$

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\$v=\\var{v}\$

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Need to ra\$v=\\var{v}\$ndomise the transformation (currently 3) perhaps between -3 to +3

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Also axis should be variable so as to see whole of graph.

\n

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Given th original formula the student enters the transformed formula

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