{"id":"cb_question_bank:8051471b-302b-47c8-97c9-c65dd28bb43c","source_id":"cb_question_bank","source_item_id":"8051471b-302b-47c8-97c9-c65dd28bb43c","external_id":null,"ibn":"08364-DC","question_id":"70753f99","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The function f is defined by f of x equals, open parenthesis, x plus 3, close parenthesis, times, open parenthesis, x plus 1, close parenthesis . The graph of f in the xy -plane is a parabola. Which of the following intervals contains the x -coordinate of the vertex of the graph of f ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">The function <span class=\"italic\">f</span> is defined by <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c19a5371bf0847a3d08f46201098d50217d380b3a5b3b660387dcd2b7bbbe44b\" alt=\"f of x equals, open parenthesis, x plus 3, close parenthesis, times, open parenthesis, x plus 1, close parenthesis\"></span></span>. The graph of <span class=\"italic\">f</span> in the <span class=\" italic \">xy</span>-plane is a parabola. Which of the following intervals contains the <span class=\" italic \">x</span>-coordinate of the vertex of the graph of <span class=\"italic\">f</span> ?</p>\n","rationale_html":"<p>Choice B is correct. The graph of a quadratic function in the <span class=\"italic\">xy</span>-plane is a parabola. The axis of symmetry of the parabola passes through the vertex of the parabola. Therefore, the vertex of the parabola and the midpoint of the segment between the two <span class=\"italic\">x</span>-intercepts of the graph have the same <span class=\"italic\">x</span>-coordinate. Since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5b2f7e63778fce5e823e48b84119e9bdc7a12a63a9a47465a711416cf944fa0b\" alt=\"f of negative 3, equals, f of negative 1, which equals 0\"></span>, the <span class=\"italic\">x</span>-coordinate of the vertex is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7f1cfbbf2bdf3c357ba6640f24ed2e5bfd713cd27e26f4d7c3227cb00043c0e9\" alt=\"the fraction with numerator negative 3 plus negative 1, and denominator 2, equals negative 2\"></span>. Of the shown intervals, only the interval in choice B contains –2. Choices A, C, and D are incorrect and may result from either calculation errors or misidentification of the graph’s <span class=\"italic\">x</span>-intercepts.</p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.635000+00:00","source_updated_at":"2023-08-02T20:25:59.635000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0490b888f59a123d9435a96ffb8a5bb16847b5a8dffeb9f7bdcce723db0ef113\" alt=\"negative 4 is less than x, which is less than negative 3\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1b05435993425dfa43b109081db05f5edbc96f8cfaaa9a1383aeb999202614d8\" alt=\"negative 3 is less than x, which is less than 1\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/005274595d16b693b53001f72cfa9c735b24592073c7ce8c7ce8426aab19f013\" alt=\"1 is less than x, which is less than 3\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/afa5263d02754c3eef24e204ebdf72866bf7d76933b3c774c55628fc31613693\" alt=\"3 is less than x, which is less than 4\"></span></span>\n          </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}}