{"id":"cb_question_bank:3fcfead5-912e-417a-9e4f-ee257489c68a","source_id":"cb_question_bank","source_item_id":"3fcfead5-912e-417a-9e4f-ee257489c68a","external_id":"375d70d6-9387-4fb7-a51e-674183bfce7c","ibn":null,"question_id":"341ba5db","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"g left parenthesis x right parenthesis equals x squared plus 55 What is the minimum value of the given function?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"g left parenthesis x right parenthesis equals x squared plus 55\"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mrow><mn>55</mn></mrow></math></p>\n<p>What is the minimum value of the given function?</p>","rationale_html":"<p style=\"text-align: left;\">Choice B is correct. For a quadratic function defined by an equation of the form <math alttext=\"g left parenthesis x right parenthesis equals a left parenthesis x minus h right parenthesis squared plus k\"><mi>g</mi><mfenced><mi>x</mi></mfenced><mo>=</mo><mi>a</mi><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mi>h</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mi>k</mi></math>, where <math alttext=\"a\"><mi>a</mi>\n</math>, <math alttext=\"h\"><mi>h</mi>\n</math>, and <math alttext=\"k\"><mi>k</mi>\n</math> are constants and <math alttext=\"a greater than 0\"><mi>a</mi><mo>&gt;</mo><mn>0</mn></math>, the minimum value of the function is <math alttext=\"k\"><mi>k</mi>\n</math>. In the given function, <math alttext=\"a equals 1\"><mrow>\n\t<mi>a</mi>\n\t<mo>=</mo>\n\t<mn>1</mn>\n</mrow>\n</math>, <math alttext=\"h equals 0\"><mrow>\n\t<mi>h</mi>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math>, and <math alttext=\"k equals 55\"><mrow>\n\t<mi>k</mi>\n\t<mo>=</mo>\n\t<mn>55</mn>\n</mrow>\n</math>. Therefore, the minimum value of the given function is <math alttext=\"55\"><mn>55</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect. This is the value of <math alttext=\"x\"><mi>x</mi>\n</math> for which the given function reaches its minimum value, not the minimum value of the function.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.828000+00:00","source_updated_at":"2023-08-02T20:25:59.828000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"0\"><mn>0</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"55\"><mn>55</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"110\"><mn>110</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"3,025\"><mn>3,025</mn>\n</math></p>","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}