// 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": [{"rulesets": {}, "extensions": ["jsxgraph"], "statement": "

This is a non-calculator question.

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

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]}}\$.

\n

{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?

", "unitTests": [], "maxValue": "answer[0]", "marks": "0.25", "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "showFeedbackIcon": true, "allowFractions": false, "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "minValue": "answer[0]", "type": "numberentry"}, {"correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "mustBeReduced": false, "variableReplacements": [], "prompt": "

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]}}\$.

\n

{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?

", "unitTests": [], "maxValue": "answer[1]", "marks": "0.25", "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "showFeedbackIcon": true, "allowFractions": false, "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "minValue": "answer[1]", "type": "numberentry"}, {"correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "mustBeReduced": false, "variableReplacements": [], "prompt": "

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?

", "unitTests": [], "maxValue": "answer[2]", "marks": "0.25", "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "showFeedbackIcon": true, "allowFractions": false, "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "minValue": "answer[2]", "type": "numberentry"}, {"correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "mustBeReduced": false, "variableReplacements": [], "prompt": "

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?

", "unitTests": [], "maxValue": "answer[3]", "marks": "0.25", "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "showFeedbackIcon": true, "allowFractions": false, "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "minValue": "answer[3]", "type": "numberentry"}], "ungrouped_variables": [], "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.

", "preamble": {"js": "", "css": ""}, "type": "question", "contributors": [{"name": "Clare Lundon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/492/"}, {"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}]}], "contributors": [{"name": "Clare Lundon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/492/"}, {"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}