{"id":"cb_practice_pdf:t11-math-m2-q22","source_id":"cb_practice_pdf","source_item_id":"t11-math-m2-q22","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":null,"form_id":"cb_practice_pdf:test-11","module_number":2,"position":22,"stem":"22 f x = - 6x^2 + 60x - 126 ^ h The function f is defined by the given equation. Which of the following equivalent forms of the equation displays the maximum value of the function as a constant or coefficient?","stimulus":"","stimulus_html":null,"stem_html":"<p>22 f x = - 6x^2 + 60x - 126 ^ h The function f is defined by the given equation. Which of the following equivalent forms of the equation displays the maximum value of the function as a constant or coefficient?</p>","rationale_html":"<p>Choice C is correct. The given equation is quadratic. The maximum value of a function defined by a quadratic equation can be displayed as a constant in the = - 2+ vertex form of the equation, f^xh a^x hh k, where the maximum value of the = function is k, which occurs when x h, and a is a constant. The given equation can be rewritten in this form by completing the square. To complete the square, =-6 2-10 -126 the given equation can be rewritten as f^xh ^x xh , which is =-6 2-10 +25 -126+6 25 =-6 -5 2+24 equivalent to f^xh ^x x h ^ h, or f^xh ^x h . This =- = =24 equation is in vertex form, where a 6, h 5, and k . Therefore, =-6 -5 2+24 24 f^xh ^x h displays the maximum value, , of the function as a constant. Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect. This form displays one of the zeros, not the maximum value, of the function as a constant. Choice D is incorrect. This form displays the zeros, not the maximum value, of the function as constants.</p>","correct_answer":["C"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>f x = - 6x^2 + 42x + 18x - 126 ^ h</p>","ord":0},{"label":"B","content_html":"<p>f x = -6x x - 7 + 18 x - 7 ^ h ^ h ^ h = - - +</p>","ord":1},{"label":"C","content_html":"<p>f x 6 x 5 24 ^ h ^ h^2</p>","ord":2},{"label":"D","content_html":"<p>f x = -6 x - 7 x - 3 ^ h ^ h^ h</p>","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}