{"id":"cb_question_bank:ceb005e4-401a-42dd-a8ac-e41da7cef3bc","source_id":"cb_question_bank","source_item_id":"ceb005e4-401a-42dd-a8ac-e41da7cef3bc","external_id":"1010a838-bf8c-4e58-8c76-a23fa7c4ee2b","ibn":null,"question_id":"6d9e01a2","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"H","score_band":6,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"f left parenthesis x right parenthesis equals 4 x squared minus 50 x plus 126 The given equation defines the function f . For what value of x does f left parenthesis x right parenthesis reach its minimum?","stimulus":"","stimulus_html":null,"stem_html":"

fx=\n\t\n\t\t4\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t-\n\t\n\t\t50\n\t\tx\n\t\n\t+\n\t126\n\n

\n

The given equation defines the function f\n. For what value of x\n does fx reach its minimum?

","rationale_html":"

The correct answer is \n\t25\n\t4\n\n. The given equation can be rewritten in the form fx=ax-h2+k, where a\n, h\n, and k\n are constants. When a>0, h\n is the value of x\n for which fx reaches its minimum. The given equation can be rewritten as fx=4x2-504x+126, which is equivalent to fx=4x2-504x+5082-5082+126. This equation can be rewritten as fx=4x-5082-5082+126, or fx=4x-5082-45082+126, which is equivalent to fx=4x-2542-1214. Therefore, \n\th\n\t=\n\t\n\t\t25\n\t\t4\n\t\n\n, so the value of x\n for which fx reaches its minimum is \n\t25\n\t4\n\n. Note that 25/4 and 6.25 are examples of ways to enter a correct answer.

","correct_answer":["25/4","6.25"],"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":[],"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}}