// Numbas version: exam_results_page_options
{"name": "Interpreting quadratic - with graph", "extensions": [], "custom_part_types": [], "resources": [["question-resources/parabola1.png", "/srv/numbas/media/question-resources/parabola1.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Interpreting quadratic - with graph", "tags": [], "metadata": {"description": "A graph is given with one intercept (negative) and a vertex (positive x and y) and from this students should be able to ascertain the axis of symmetry and equation (given that the leading coefficent of x is -1)", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>The graph of the quadratic function $f(x) = c + bx - x^2$ intersects the $x$-axis at the point A = ({x_int1},0) and has it's vertex at point B = ({x_vert},{y_vert})</p>\n<p><img src=\"resources/question-resources/parabola1.png\"/></p>", "advice": "<p>In part (a) you can calculate the axis of symmetry from the x-coordinate of the vertex {x_vert}. Don't forget to put in the form of an equation for a vertical line.</p>\n<p>$x = $ {x_vert}</p>\n<p>In part (b) use the formula that the axis of symmetry has equation $x = \\frac {-b}{2a}$. Rearranging and substituting a with -1.</p>\n<p>$b = 2 \\times&nbsp;${x_vert}&nbsp;</p>\n<p>$b =$ {b}</p>\n<p>In part (c) you now know the value of $b$ and have two coordinates to work with, so you can find&nbsp;$c$ by substitution.</p>\n<p>EITHER</p>\n<p>$0 = c +$ {b} $\\times${x_int1} $-(${x_int1}$)^2$</p>\n<p>$c = ($&nbsp;{x_int1}$)^2$ $-${b}$\\times${x_int1}</p>\n<p>$c =$ {c}</p>\n<p>OR</p>\n<p>{y_vert} $= c +$ {b} $\\times${x_vert} $-${x_vert}$^2$</p>\n<p>$c =$&nbsp;{x_vert}$^2$ $-${b}$\\times${x_vert} $+$ {y_vert}</p>\n<p>$c =$ {c}</p>", "rulesets": {}, "extensions": [], "variables": {"x_int1": {"name": "x_int1", "group": "Ungrouped variables", "definition": "random(-6 .. -1#1)", "description": "<p>left intercept with the x-axis, must be negative to agree with diagram.</p>", "templateType": "randrange"}, "x_vert": {"name": "x_vert", "group": "Ungrouped variables", "definition": "random(2 .. 4#1)", "description": "<p>x-coordinate of vertex, must be positive to agree with diagram.</p>", "templateType": "randrange"}, "x_int2": {"name": "x_int2", "group": "Ungrouped variables", "definition": "2*x_vert - x_int1", "description": "<p>right intercept with the x-axis, calculated based on vertex</p>", "templateType": "anything"}, "y_vert": {"name": "y_vert", "group": "Ungrouped variables", "definition": "-(x_vert - x_int1)*(x_vert - x_int2)", "description": "<p>y - coordinate of vertex, calculated from intercepts and leading coefficient of $x^2$ being -1</p>", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "2*x_vert", "description": "<p>coefficient of x</p>", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "-x_int1*x_int2", "description": "<p>constant term</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x_int1", "x_vert", "x_int2", "y_vert", "b", "c"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the&nbsp;<strong>equation</strong>&nbsp;of the axis of symmetry of $f$</p>", "answer": "x[ ]*=[ ]*{x_vert}", "displayAnswer": "x = {x_vert}", "matchMode": "regex"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the value of $b$.</p>", "minValue": "{b}", "maxValue": "{b}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the value of $c$.</p>", "minValue": "{c}", "maxValue": "{c}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Johnathan Gregg", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4974/"}]}]}], "contributors": [{"name": "Johnathan Gregg", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4974/"}]}