// 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": "

You should be using the graphs to answer this question - there is no need to do any calculations or algebraic things.

\n

See 4.1 for background on quadratics and see 1.1 for what the word solution means.

", "name": "Algebra: number of solutions of quadratic based on graph", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

A quadratic is given and sketched. Based on the sketch, task is to determine the number of solutions to the equation \$f(x)=0\$.

"}, "extensions": ["jsxgraph"], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"js": "", "css": ""}, "ungrouped_variables": [], "statement": "

This is a non-calculator question.

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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]}}\$.

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{plot(0,a[0],b[0],c[0])}

\n

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?

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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]}}\$.

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{plot(0,a[1],b[1],c[1])}

\n

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?

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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]}}\$.

\n

{plot(0,a[2],b[2],c[2])}

\n

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?

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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]}}\$.

\n

{plot(0,a[3],b[3],c[3])}

\n

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?

", "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/"}]}