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{"name": "PreCal Application of Polynomials Quadratic Vertex Form", "extensions": [], "custom_part_types": [], "resources": [["question-resources/img_0101_rainbow.jpg", "/srv/numbas/media/question-resources/img_0101_rainbow.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "rulesets": {}, "variables": {"hg": {"description": "", "name": "hg", "definition": "h+hMove", "group": "Ungrouped variables", "templateType": "anything"}, "bH": {"description": "", "name": "bH", "definition": "2*a*h", "group": "Ungrouped variables", "templateType": "anything"}, "cg": {"description": "", "name": "cg", "definition": "kg-a*hg^2", "group": "Ungrouped variables", "templateType": "anything"}, "aH": {"description": "", "name": "aH", "definition": "-a", "group": "Ungrouped variables", "templateType": "anything"}, "hMove": {"description": "", "name": "hMove", "definition": "random(1..50#0.25)", "group": "Ungrouped variables", "templateType": "anything"}, "a": {"description": "", "name": "a", "definition": "random(0.01..0.5#0.01)", "group": "Ungrouped variables", "templateType": "anything"}, "rhLeft": {"description": "", "name": "rhLeft", "definition": "precround((-bH+sqrt(bH^2-4*aH*cH))/(2*aH),3)", "group": "Ungrouped variables", "templateType": "anything"}, "dLeft": {"description": "<p>d</p>", "name": "dLeft", "definition": "precround(gLeft-rhLeft,3)", "group": "Ungrouped variables", "templateType": "anything"}, "kg": {"description": "", "name": "kg", "definition": "k-kMove", "group": "Ungrouped variables", "templateType": "anything"}, "bg": {"description": "", "name": "bg", "definition": "2*a*hg", "group": "Ungrouped variables", "templateType": "anything"}, "gLeft": {"description": "", "name": "gLeft", "definition": "precround((-bg+sqrt(bg^2-4*ag*cg))/(2*ag),3)", "group": "Ungrouped variables", "templateType": "anything"}, "h": {"description": "", "name": "h", "definition": "random(-50..50#0.25 except 0)", "group": "Ungrouped variables", "templateType": "anything"}, "ag": {"description": "<p>ag</p>", "name": "ag", "definition": "-a", "group": "Ungrouped variables", "templateType": "anything"}, "gRight": {"description": "", "name": "gRight", "definition": "precround((-bg-sqrt(bg^2-4*ag*cg))/(2*ag),3)", "group": "Ungrouped variables", "templateType": "anything"}, "dRight": {"description": "", "name": "dRight", "definition": "precround(gRight-rhLeft,3)", "group": "Ungrouped variables", "templateType": "anything"}, "k": {"description": "", "name": "k", "definition": "random(2..15#0.05)", "group": "Ungrouped variables", "templateType": "anything"}, "kMove": {"description": "", "name": "kMove", "definition": "random(0.2..0.75#0.01)*k", "group": "Ungrouped variables", "templateType": "anything"}, "rhRight": {"description": "", "name": "rhRight", "definition": "(-bH-sqrt(bH^2-4*aH*cH))/(2*aH)", "group": "Ungrouped variables", "templateType": "anything"}, "cH": {"description": "", "name": "cH", "definition": "k-a*h^2", "group": "Ungrouped variables", "templateType": "anything"}}, "parts": [{"scripts": {}, "variableReplacements": [], "showCorrectAnswer": true, "useCustomName": false, "type": "gapfill", "extendBaseMarkingAlgorithm": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "customMarkingAlgorithm": "", "gaps": [{"scripts": {}, "showCorrectAnswer": true, "correctAnswerFraction": false, "minValue": "dLeft", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "maxValue": "dLeft", "marks": 1, "adaptiveMarkingPenalty": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "variableReplacements": [], "type": "numberentry", "useCustomName": false, "unitTests": [], "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "showFractionHint": true, "customName": ""}, {"scripts": {}, "showCorrectAnswer": true, "correctAnswerFraction": false, "minValue": "dRight", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "maxValue": "dRight", "marks": 1, "adaptiveMarkingPenalty": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "variableReplacements": [], "type": "numberentry", "useCustomName": false, "unitTests": [], "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "showFractionHint": true, "customName": ""}], "showFeedbackIcon": true, "marks": 0, "prompt": "<p>The distances in kilometers from the leprachaun's cottage to the pots of gold are:</p>\n<p>[[0]]&nbsp;<em>(the shortest distance)</em></p>\n<p>[[1]]&nbsp;<em>(the largest distance)</em></p>", "adaptiveMarkingPenalty": 0, "customName": ""}], "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "functions": {}, "ungrouped_variables": ["a", "h", "k", "hMove", "kMove", "aH", "bH", "cH", "rhRight", "rhLeft", "ag", "hg", "kg", "bg", "cg", "gLeft", "gRight", "dLeft", "dRight"], "name": "PreCal Application of Polynomials Quadratic Vertex Form", "statement": "<p><img src=\"resources/question-resources/img_0101_rainbow.jpg\"/></p>\n<p><em>(Image taken from&nbsp;<a href=\"https://cottagecapers.com/tag/rainbows/\">https://cottagecapers.com/tag/rainbows/</a>)</em></p>\n<p><em></em></p>\n<p>A very lucky and mathematical leprachaun decided to hide his pot of gold in a location other than the known location \"at the end of the rainbow\".&nbsp; Also, being a believer in the Good Book, decided not to put all his eggs in one basket so to speak.&nbsp; So, he has buried his gold in two locations where his transformed rainbow touches the ground.&nbsp; The visible rainbow is defined by the function $\\simplify{ f(x)= -{a}*(x-{h})^2 + {k} }$, where the leftmost point touches the ground at his little humble cottage.&nbsp; If the visible rainbow is moved to the right by $\\var{hMove}$ km, and the maximum height of the rainbox is moved down by $\\var{kMove}$ km, then the ends of the rainbow will mark the location of his two buried pots of gold.&nbsp; What is the distance from his house to each of the pots of gold?</p>\n<p><em><strong>(Hint:&nbsp; The clever little leprachaun used Desmos graphing calculator for his calculations!)</strong></em></p>", "metadata": {"description": "", "licence": "All rights reserved"}, "tags": [], "extensions": [], "advice": "", "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}]}]}], "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}]}