{"id":"cb_practice_pdf:t7-math-m1-q27","source_id":"cb_practice_pdf","source_item_id":"t7-math-m1-q27","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":"spr","answer_source":"rationale","layout_warning":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-7","module_number":1,"position":27,"stem":"= (x−2)(x+15) f(x) The function f is defined by the given equation. For f(x) what value of x does reach its minimum? OP","stimulus":"","stimulus_html":null,"stem_html":"<p>= (x−2)(x+15) f(x) The function f is defined by the given equation. For f(x) what value of x does reach its minimum? OP</p>","rationale_html":"<p>13 - The correct answer is 2. The value of x for which f^xh reaches its minimum can = - 2+ be found by rewriting the given equation in the form f^xh ^x hh k, where f^xh reaches its minimum, k, when the value of x is h. The given equation, = -2 +15 = 2+13 -30 f^xh ^x h^x h, can be rewritten as f^xh x x . By completing the = 2+13 + 13 2 -30- 13 2 square, this equation can be rewritten as f^xh ax x ` 2 j k ` 2 j , 13 2 289 13 2 289 = + - = - - - which is equivalent to f^xh `x 2 j 4 , or f^xh `x ` 2 jj 4 . Therefore, 13 - f^xh reaches its minimum when the value of x is 2. Note that -13/2 and -6.5 are examples of ways to enter a correct answer. = Alternate approach: The graph of y f^xh in the xy-plane is a parabola. The value of x for the vertex of a parabola is the x-value of the midpoint between the two = -2 +15 x-intercepts of the parabola. Since it’s given that f^xh ^x h^x h, it follows = = that the two x-intercepts of the graph of y f^xh in the xy-plane occur when x 2 =-15 2,0 -15,0 and x , or at the points ^ h and ^ h. The midpoint between two points, ^x 1 , y 1 h and ^x 2 , y 2 h, is c x1+ 2 x2, y1+ 2 y2 m. Therefore, the midpoint between 2,0 -15,0 2-15,0+0 - 13,0 ^ h and ^ h is b 2 2 l, or b 2 l. It follows that f^xh reaches its 13 - minimum when the value of x is 2. Note that -13/2 and -6.5 are examples of ways to enter a correct answer. 38 SAT PRACTICE TEST #7 ANSWER EXPLANATIONS</p>","correct_answer":["2"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[],"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}}