{"id":"cb_question_bank:84c39d57-3c8f-4189-8dda-698cd04521fb","source_id":"cb_question_bank","source_item_id":"84c39d57-3c8f-4189-8dda-698cd04521fb","external_id":null,"ibn":"09291-DC","question_id":"6676f055","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"An engineer wanted to identify the best angle for a cooling fan in an engine in order to get the greatest airflow. The engineer discovered that the function above models the airflow f of theta , in cubic feet per minute, as a function of the angle of the fan theta , in degrees. According to the model, what angle, in degrees, gives the greatest airflow?","stimulus":"f of theta equals, negative 0 point 2 8, times, open parenthesis, theta minus 27, close parenthesis, squared, plus 880","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2b1027fd81b8261365c0337239d457679af77424498f94ec1c8eab8a82872446\" alt=\"f of theta equals, negative 0 point 2 8, times, open parenthesis, theta minus 27, close parenthesis, squared, plus 880\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">An engineer wanted to identify the best angle for a cooling fan in an engine in order to get the greatest airflow. The engineer discovered that the function above models the airflow <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c6878c6b35b766ed70635361a50c8631916db17d69095614dea6dfed36f342dc\" alt=\"f of theta\"></span></span>, in cubic feet per minute, as a function of the angle of the fan <span class=\"italic\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/15bc6980b2f2e28aabc9cab81cfde8f900e7fec8d3d419d2f126edac89be54cc\" alt=\"theta\"></span></span><span class=\"italic\"></span>, in degrees. According to the model, what angle, in degrees, gives the greatest airflow?</p>\n","rationale_html":"<p>Choice C is correct. The function&nbsp;<span class=\"italic\">f</span>&nbsp;is quadratic, so it will have either a maximum or a minimum at the vertex of the graph. Since the coefficient of the quadratic term&nbsp;(–0.28)&nbsp;is negative, the vertex will be at a maximum. The equation <span class=\"italic\">f</span>(<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/15bc6980b2f2e28aabc9cab81cfde8f900e7fec8d3d419d2f126edac89be54cc\" alt=\"theta\"></span>) = –0.28(<span class=\"italic\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/15bc6980b2f2e28aabc9cab81cfde8f900e7fec8d3d419d2f126edac89be54cc\" alt=\"theta\"></span></span> – 27)<sup>2</sup> + 880 is given in vertex form, so the vertex is at&nbsp;<span class=\"italic\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/15bc6980b2f2e28aabc9cab81cfde8f900e7fec8d3d419d2f126edac89be54cc\" alt=\"theta\"></span></span> = 27. Therefore,&nbsp;an angle of 27 degrees&nbsp;gives the greatest airflow.</p><p>Choices A and B are&nbsp;incorrect and may be the result of&nbsp;misidentifying&nbsp;which value in a quadratic equation in vertex form represents the vertex.&nbsp;Choice D is incorrect.&nbsp;This choice identifies the maximum value of <span class=\"italic\">f</span>(<span class=\"italic\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/15bc6980b2f2e28aabc9cab81cfde8f900e7fec8d3d419d2f126edac89be54cc\" alt=\"theta\"></span></span>) rather than the value of&nbsp;<span class=\"italic\"></span><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/15bc6980b2f2e28aabc9cab81cfde8f900e7fec8d3d419d2f126edac89be54cc\" alt=\"theta\"></span> for which <span class=\"italic\">f</span>(<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/15bc6980b2f2e28aabc9cab81cfde8f900e7fec8d3d419d2f126edac89be54cc\" alt=\"theta\"></span><span class=\"italic\"></span>) is maximized.</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.637000+00:00","source_updated_at":"2023-08-02T20:25:59.637000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">–0.28</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">0.28</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">27</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">880</p>\n","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}}