// Numbas version: finer_feedback_settings
{"name": "Solving Quadratic Equations using the Quadratic Formula", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"disc2": {"definition": "b[1]^2-4*a[1]*c[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "disc2", "description": ""}, "disc3": {"definition": "b[2]^2-4*a[2]*c[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "disc3", "description": ""}, "a": {"definition": "repeat(random(1..5),4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "b": {"definition": "repeat(random(-10..10),4)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "c": {"definition": "repeat(random(-20..20),4)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "ansplus": {"definition": "siground((-b[0] + sqrt(b[0]^2-4a[0]*c[0]))/(2*a[0]),4)", "templateType": "anything", "group": "Ungrouped variables", "name": "ansplus", "description": ""}, "ansmin": {"definition": "siground((-b[0] - sqrt(b[0]^2-4a[0]*c[0]))/(2*a[0]),4)", "templateType": "anything", "group": "Ungrouped variables", "name": "ansmin", "description": ""}, "disc1": {"definition": "b[0]^2-4*a[0]*c[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "disc1", "description": ""}, "disc4": {"definition": "b[3]^2-4*a[3]*c[3]", "templateType": "anything", "group": "Ungrouped variables", "name": "disc4", "description": ""}}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Selection of Quadratic Equations to Solve</p>"}, "statement": "<p>Solve&nbsp;the following quadratic&nbsp;equations&nbsp;with the quadratic formula:<strong> &nbsp;</strong><numerator>$x = \\dfrac{-b\\pm\\sqrt{b^2-4ac}}{2a}$</numerator></p>\n<p></p>\n<p style=\"text-align: left;\"></p>", "name": "Solving Quadratic Equations using the Quadratic Formula", "variablesTest": {"maxRuns": "167", "condition": "disc1>=0\nand\ndisc2>=0\nand\ndisc3>=0\nand\ndisc4>=0"}, "extensions": ["stats"], "rulesets": {}, "tags": [], "advice": "<p><strong>Worked example using Part a:</strong></p>\n<p style=\"text-align: center;\">Find the roots of $\\simplify{{a[0]}*x^2+{b[0]}*x+{c[0]}}=0$.</p>\n<p>The quadratic formula is given by&nbsp;$x = \\dfrac{-b\\pm\\sqrt{b^2-4ac}}{2a}$</p>\n<p style=\"text-align: left;\">To solve this, simply input the numbers from the equation into the formula, defining the coefficient of $x^2$ as $a$, the coefficient of $x$ as $b$, and the constant as $c$.</p>\n<p style=\"text-align: left;\">Here, &nbsp;$x=$ &nbsp;<fraction><numerator>$-(\\var{b[0]})$$\\pm$$\\sqrt{(\\var{b[0]})^2-4(\\var{a[0]}\\times\\var{c[0]})}$</numerator><denominator>$2\\times\\var{a[0]}$</denominator></fraction></p>\n<p style=\"text-align: left;\">Inputting these figures into a calculator, starting with the minus sign before the root, gives: &nbsp;$x=\\var{ansmin}$,</p>\n<p style=\"text-align: left;\">and using the positive root version gives the other solution: &nbsp;$x=\\var{ansplus}$.</p>", "functions": {}, "variable_groups": [], "preamble": {"js": "document.createElement('fraction');\ndocument.createElement('numerator');\ndocument.createElement('denominator');", "css": "fraction {\n  display: inline-block;\n  vertical-align: middle;\n}\nfraction > numerator, fraction > denominator {\n  float: left;\n  width: 100%;\n  text-align: center;\n  line-height: 2.5em;\n}\nfraction > numerator {\n  border-bottom: 1px solid;\n  padding-bottom: 5px;\n}\nfraction > denominator {\n  padding-top: 5px;\n}\nfraction input {\n    line-height: 1em;\n}\n\nfraction .part {\n    margin: 0;\n}\n\n.table-responsive, .fractiontable {\n  display:inline-block;\n}\n.fractiontable {\n  padding: 0; \n  border: 0;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n\n.fractiontable tr {\n    height: 3em;\n}"}, "parts": [{"variableReplacements": [], "scripts": {}, "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "gaps": [{"maxValue": "(-{b[0]}-sqrt({b[0]}^2-4*{a[0]}*{c[0]}))/(2*{a[0]})+0.0005", "precision": "4", "mustBeReducedPC": 0, "scripts": {}, "marks": "1", "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "type": "numberentry", "variableReplacements": [], "precisionType": "sigfig", "strictPrecision": false, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showPrecisionHint": false, "showFeedbackIcon": true, "correctAnswerFraction": false, "precisionMessage": "<p>You have not given your answer to the correct number of significant figures.</p>", "precisionPartialCredit": "50", "minValue": "(-{b[0]}-sqrt({b[0]}^2-4*{a[0]}*{c[0]}))/(2*{a[0]})-0.0005"}, {"maxValue": "(-{b[0]}+sqrt({b[0]}^2-4*{a[0]}*{c[0]}))/(2*{a[0]})+0.0005", "precision": "4", "mustBeReducedPC": 0, "scripts": {}, "marks": 1, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "type": "numberentry", "variableReplacements": [], "precisionType": "sigfig", "strictPrecision": false, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showPrecisionHint": false, "showFeedbackIcon": true, "correctAnswerFraction": false, "precisionMessage": "<p>You have not given your answer to the correct number of significant figures.</p>", "precisionPartialCredit": "50", "minValue": "(-{b[0]}+sqrt({b[0]}^2-4*{a[0]}*{c[0]}))/(2*{a[0]})-0.0005"}], "type": "gapfill", "prompt": "<p>Find the values of $x$ that solve the equation $\\simplify{{a[0]}*x^2+{b[0]}*x+{c[0]}}=0$.</p>\n<p>Give your answers in ascending order (ie smallest first) to four significant figures.</p>\n<p>$x=$&nbsp;[[0]] and $x=$&nbsp;[[1]]</p>\n<p></p>"}, {"variableReplacements": [], "scripts": {}, "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "gaps": [{"maxValue": "(-{b[1]}-sqrt({b[1]}^2-4*{a[1]}*{c[1]}))/(2*{a[1]})+0.0005", "precision": "4", "mustBeReducedPC": 0, "scripts": {}, "marks": "1", "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "type": "numberentry", "variableReplacements": [], "precisionType": "sigfig", "strictPrecision": false, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showPrecisionHint": false, "showFeedbackIcon": true, "correctAnswerFraction": false, "precisionMessage": "<p>You have not given your answer to the correct number of significant figures.</p>", "precisionPartialCredit": "50", "minValue": "(-{b[1]}-sqrt({b[1]}^2-4*{a[1]}*{c[1]}))/(2*{a[1]})-0.0005"}, {"maxValue": "(-{b[1]}+sqrt({b[1]}^2-4*{a[1]}*{c[1]}))/(2*{a[1]})+0.0005", "precision": "4", "mustBeReducedPC": 0, "scripts": {}, "marks": 1, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "type": "numberentry", "variableReplacements": [], "precisionType": "sigfig", "strictPrecision": false, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showPrecisionHint": false, "showFeedbackIcon": true, "correctAnswerFraction": false, "precisionMessage": "<p>You have not given your answer to the correct number of significant figures.</p>", "precisionPartialCredit": "50", "minValue": "(-{b[1]}+sqrt({b[1]}^2-4*{a[1]}*{c[1]}))/(2*{a[1]})-0.0005"}], "type": "gapfill", "prompt": "<p>Find the roots of $\\simplify{{a[1]}*x^2+{b[1]}*x+{c[1]}}=0$.</p>\n<p>Give your answers in ascending order to four significant figures.</p>\n<p>$x=$&nbsp;[[0]] and $x=$&nbsp;[[1]]</p>\n<p></p>"}, {"variableReplacements": [], "scripts": {}, "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "gaps": [{"maxValue": "(-{b[2]}-sqrt({b[2]}^2-4*{a[2]}*{c[2]}))/(2*{a[2]})+0.0005", "precision": "4", "mustBeReducedPC": 0, "scripts": {}, "marks": "1", "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "type": "numberentry", "variableReplacements": [], "precisionType": "sigfig", "strictPrecision": false, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showPrecisionHint": false, "showFeedbackIcon": true, "correctAnswerFraction": false, "precisionMessage": "<p>You have not given your answer to the correctnumber of significant figures.</p>", "precisionPartialCredit": "50", "minValue": "(-{b[2]}-sqrt({b[2]}^2-4*{a[2]}*{c[2]}))/(2*{a[2]})-0.0005"}, {"maxValue": "(-{b[2]}+sqrt({b[2]}^2-4*{a[2]}*{c[2]}))/(2*{a[2]})+0.0005", "precision": "4", "mustBeReducedPC": 0, "scripts": {}, "marks": 1, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "type": "numberentry", "variableReplacements": [], "precisionType": "sigfig", "strictPrecision": false, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showPrecisionHint": false, "showFeedbackIcon": true, "correctAnswerFraction": false, "precisionMessage": "<p>You have not given your answer to the correct number of significant figures.</p>", "precisionPartialCredit": "50", "minValue": "(-{b[2]}+sqrt({b[2]}^2-4*{a[2]}*{c[2]}))/(2*{a[2]})-0.0005"}], "type": "gapfill", "prompt": "<p>Find the roots of $\\simplify{{a[2]}*x^2+{b[2]}*x+{c[2]}}=0$.</p>\n<p>Give your answers in ascending order to four significant figures.</p>\n<p>$x=$&nbsp;[[0]] and $x=$&nbsp;[[1]]</p>\n<p></p>"}, {"variableReplacements": [], "scripts": {}, "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "gaps": [{"maxValue": "(-{b[3]}-sqrt({b[3]}^2-4*{a[3]}*{c[3]}))/(2*{a[3]})+0.0005", "precision": "4", "mustBeReducedPC": 0, "scripts": {}, "marks": "1", "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "type": "numberentry", "variableReplacements": [], "precisionType": "sigfig", "strictPrecision": false, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showPrecisionHint": false, "showFeedbackIcon": true, "correctAnswerFraction": false, "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "precisionPartialCredit": "50", "minValue": "(-{b[3]}-sqrt({b[3]}^2-4*{a[3]}*{c[3]}))/(2*{a[3]})-0.0005"}, {"maxValue": "(-{b[3]}+sqrt({b[3]}^2-4*{a[3]}*{c[3]}))/(2*{a[3]})+0.0005", "precision": "4", "mustBeReducedPC": 0, "scripts": {}, "marks": 1, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "type": "numberentry", "variableReplacements": [], "precisionType": "sigfig", "strictPrecision": false, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showPrecisionHint": false, "showFeedbackIcon": true, "correctAnswerFraction": false, "precisionMessage": "You have not given your answer to the correct precision.", "precisionPartialCredit": "50", "minValue": "(-{b[3]}+sqrt({b[3]}^2-4*{a[3]}*{c[3]}))/(2*{a[3]})-0.0005"}], "type": "gapfill", "prompt": "<p>Find the roots of $\\simplify{{a[3]}*x^2+{b[3]}*x+{c[3]}}=0$.</p>\n<p>Give your answers in ascending order to four significant figures.</p>\n<p>$x=$&nbsp;[[0]] and $x=$&nbsp;[[1]]</p>\n<p></p>"}], "ungrouped_variables": ["a", "b", "c", "disc1", "disc2", "disc3", "disc4", "ansmin", "ansplus"], "type": "question", "contributors": [{"name": "Hannah Bartholomew", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/530/"}]}]}], "contributors": [{"name": "Hannah Bartholomew", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/530/"}]}