{"id":"cb_question_bank:4fd8957f-8711-4a35-ab7c-dce0712fd4b5","source_id":"cb_question_bank","source_item_id":"4fd8957f-8711-4a35-ab7c-dce0712fd4b5","external_id":null,"ibn":"00664-DC","question_id":"a1bf1c4e","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which of the following is equivalent to the expression above?","stimulus":"x squared, plus 6 x, plus 4","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/e0e05b9e6e7c8c45de733b37577eba2a3f65a33ccddbebc16b27ab7a6efa9823\" alt=\"x squared, plus 6 x, plus 4\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">Which of the following is equivalent to the expression above?</p>\n","rationale_html":"<p>Choice B is correct. The given quadratic expression is in standard form, and each answer choice is in vertex form. Completing the square converts the expression from standard form to vertex form. The first step is to rewrite the expression as follows: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1b3084c6aad1ea8b412462d0fbbec0aa457894bd7e8ccf2dd634f7545500b7f8\" alt=\"x squared, plus 6 x, plus 4, equals, x squared, plus 6 x, plus 9, plus 4, minus 9\"></span>. The first three terms of the revised expression can be rewritten as a perfect square as follows: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2685a2db83b30951b2d8717831989f3c58fa7d0091f0c3a2ebae3cbd8a30fc2d\" alt=\"x squared, plus 6 x, plus 9, plus 4, minus 9, equals, open parenthesis, x plus 3, close parenthesis, squared, plus 4, minus 9\"></span>. Combining the constant terms gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/62addd70a513e15801705b26c51abdf20ef234ff7a64f16ac91744722a7d540c\" alt=\"open parenthesis, x plus 3, close parenthesis, squared, minus 5\"></span>.</p><p>Choice A is incorrect. Squaring the binomial and simplifying the expression in choice A gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/44263c12d7f05923a4c086b6e36bb5c4571b62bef8cced2462c05e29239b2d7f\" alt=\"x squared, plus 6 x, plus 9, plus 5\"></span>. Combining like terms gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/571d5ba26ec568e896da63260ce3c2f3d06ca1bbf0ccc19c1d448702900cd9ff\" alt=\"x squared, minus 6 x, plus 14\"></span>, not <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e0e05b9e6e7c8c45de733b37577eba2a3f65a33ccddbebc16b27ab7a6efa9823\" alt=\"x squared, plus 6 x, plus 4\"></span>. Choice C is incorrect. Squaring the binomial and simplifying the expression in choice C gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9244a0e05e808c0c6e69ba9cc64cd88928122c8c9f39be732cdb8d37e47f04d2\" alt=\"x squared, minus 6 x, plus 9, plus 5\"></span>. Combining like terms gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9d6b0bc1dd7c084d3b0e9759f162f589a3b7f3b1ecb4b695fe1bf0da12052f2d\" alt=\"x squared, minus 6 x, plus 14\"></span>, not <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e0e05b9e6e7c8c45de733b37577eba2a3f65a33ccddbebc16b27ab7a6efa9823\" alt=\"x squared, plus 6 x, plus 4\"></span>. Choice D is incorrect. Squaring the binomial and simplifying the expression in choice D gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0951fbf4c0f824e6c8fb4aa5ea3a1775c65de7c5fa006e26ea68f8f5a20bd185\" alt=\"x squared, minus 6 x, plus 9, minus 5\"></span>. Combining like terms gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/10de5ce7a8a0d34533e4e14542a214ff6bed87a53857d67ba59a2b925578ea6a\" alt=\"x squared, minus 6 x, plus 4\"></span>, not <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e0e05b9e6e7c8c45de733b37577eba2a3f65a33ccddbebc16b27ab7a6efa9823\" alt=\"x squared, plus 6 x, plus 4\"></span>.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.614000+00:00","source_updated_at":"2023-08-02T20:25:59.614000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">(<span class=\"italic\">x</span> + 3)<sup>2</sup> + 5</span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">(<span class=\"italic\">x</span> + 3)<sup>2</sup> – 5</span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">(<span class=\"italic\">x</span> – 3)<sup>2</sup> + 5</span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">(<span class=\"italic\">x</span> – 3)<sup>2</sup> – 5</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}}