{"id":"cb_practice_pdf:t8-math-m1-q20","source_id":"cb_practice_pdf","source_item_id":"t8-math-m1-q20","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":null,"form_id":"cb_practice_pdf:test-8","module_number":1,"position":20,"stem":"y = x^2 −14x+22 The given equation relates the variables x and y. For what value of x does the value of y reach its minimum?","stimulus":"","stimulus_html":null,"stem_html":"<p>y = x^2 −14x+22 The given equation relates the variables x and y. For what value of x does the value of y reach its minimum?</p>","rationale_html":"<p>= 2+ + The correct answer is 7. When an equation is of the form y ax bx c, where a, =- b b, and c are constants, the value of y reaches its minimum when x . Since 2a = 2+ + = =-14 the given equation is of the form y ax bx c, it follows that a 1, b , and c = 22. Therefore, the value of y reaches its minimum when x =-^2 -1 1 4 h, or x = 7. ^ h</p>","correct_answer":["7"],"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}}