{"id":"cb_question_bank:0aaae3be-ed52-47ec-8e45-9e283d37092b","source_id":"cb_question_bank","source_item_id":"0aaae3be-ed52-47ec-8e45-9e283d37092b","external_id":null,"ibn":"038001-DC","question_id":"91e7ea5e","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 quadratic function h is defined as shown. In the xy -plane, the graph of y equals, h of x intersects the x -axis at the points with coordinates 0 comma 0 and t comma 0 , where t is a constant. What is the value of t ?","stimulus":"h of x equals, 2 times, open parenthesis, x minus 4, close parenthesis, squared, minus 32","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/eaecffb8bf68c264bf754740153d80eb404cc92510a123818f967a68e4a145bc\" alt=\"h of x equals, 2 times, open parenthesis, x minus 4, close parenthesis, squared, minus 32\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">The quadratic function <span class=\"italic\">h</span> is defined as shown. In the <span class=\"italic \">xy</span>-plane, the graph of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/01dad43d432a687d231ff42df4f77294a187cbda324e65355238edefd6b11057\" alt=\"y equals, h of x \"></span> intersects the <span class=\"italic \">x</span>-axis at the points <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5d9546145044d67f4c5d0648e8663a351f932cd21526a7309901dbb9e25d27fb\" alt=\"with coordinates 0 comma 0 \"></span><span class=\"math_expression \"></span>and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/55b1a339ce07d4ca558fdabb54a6702f973fb323c8652a280676e2afcc286f51\" alt=\"t comma 0\"></span>, where <span class=\"italic\">t</span> is a constant. What is the value of <span class=\"italic\">t </span>?</p>\n","rationale_html":"<p>Choice D is correct. It’s given that the graph of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d7e0456b85a408288d5003af6103c9b248a47c134d4b1e51ee27ebbc49dd2451\" alt=\"y equals, h of x \"></span> intersects the <span class=\"italic\">x</span>-axis at <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d025d5d28279edb5c1e9ce6dbf942cee3cc3caaee927a6a6932dfe130c7aac9b\" alt=\"the point with coordinates 0 comma 0 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b21394375368276b53b733f4edc894117696c860cbb4f47ff53b42c765e8db7e\" alt=\"the point with coordinates t comma 0 \"></span>, where <span class=\"italic\">t</span> is a constant. Since this graph intersects the <span class=\"italic\">x</span>-axis when <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ce672c12451ce6d730167e9763ac3e67a5ed07d54cba747ed2f59adb20d5d205\" alt=\"y equals 0 \"></span> or when <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ee3b825dc7229703ae6d2ec12f41cbf44bfc260937f0c8299e926377a018a84a\" alt=\"h of x equals 0\"></span>, it follows that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/826f2141276d377b4a3ac97da40d0fb9b8928a78d1a321c7337eaa082ca1653e\" alt=\"h of 0 equals 0 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/89928e358b7a0859183ecebac503038f24bf20d3f6091d4d36e9cc03f71a2df3\" alt=\"h of t equals 0\"></span>. If <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/89928e358b7a0859183ecebac503038f24bf20d3f6091d4d36e9cc03f71a2df3\" alt=\"h of t equals 0\"></span>, then <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ab4ff00202e92d0ce59e886d087e16f6dc8c8caaa51e56bc6cff5eec216401ae\" alt=\"0 equals, 2 times, open parenthesis, t minus 4, close parenthesis, squared, minus 32\"></span>. Adding 32 to both sides of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dbebab259aa09fc7cf4d0e4512c22f6d053772fd511ac497f8e27151113bc7a0\" alt=\"32 equals, 2 times, open parenthesis, t minus 4, close parenthesis, squared\"></span>. Dividing both sides of this equation by 2 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c5394c2f8dcce46834fffb9ab3cdb54983e01cbfcf4124b7ce3ab1a1b100a890\" alt=\"16 equals, open parenthesis, t minus 4, close parenthesis, squared\"></span>. Taking the square root of both sides of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/53730dec1bfc6e3a44eca3b0d72e05ce776953bd1e07cdb36f6fc58b11d0b855\" alt=\"4 equals, t minus 4\"></span>. Adding 4 to both sides of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c2b61b159ca97b93bf100a1d92531f60ea67bb9fd471182e721a9d8f38f7ada6\" alt=\"8 equals t\"></span>. Therefore, the value of <span class=\"italic\">t</span> is 8.</p><p>Choices A, B, and C are incorrect and may result from calculation errors.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.627000+00:00","source_updated_at":"2023-08-02T20:25:59.627000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">1</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">2</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">4</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">8</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}}