{"id":"cb_question_bank:e72ae0ec-edbf-47de-bbc0-5c50155b1bfb","source_id":"cb_question_bank","source_item_id":"e72ae0ec-edbf-47de-bbc0-5c50155b1bfb","external_id":null,"ibn":"019546-DC","question_id":"7eed640d","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The quadratic function above models the height above the ground h , in feet, of a projectile x seconds after it had been launched vertically. If y equals h of x is graphed in the xy -plane, which of the following represents the real-life meaning of the positive x -intercept of the graph?","stimulus":"h of x equals, negative 16 x squared, plus 100 x, plus 10","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/a7d89bf37c08de7d2f63f236fcc7ac2c39a0be41ecc30b9ca27ea9e2581c69c0\" alt=\"h of x equals, negative 16 x squared, plus 100 x, plus 10\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">The quadratic function above models the height above the ground <span class=\"italic\">h</span>, in feet, of a projectile <span class=\"italic\">x</span> seconds after it had been launched vertically. If <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/01dad43d432a687d231ff42df4f77294a187cbda324e65355238edefd6b11057\" alt=\"y equals h of x\"></span></span> is graphed in the <span class=\"italic\"><span class=\" italic \">xy</span></span>-plane, which of the following represents the real-life meaning of the positive <span class=\"italic\"><span class=\" italic \">x</span></span>-intercept of the graph?</p>\n","rationale_html":"<p>Choice D is correct. The positive <span class=\"italic\">x</span>-intercept of 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> is a point <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/338db7e3a31d3afebe84d6ca556e60cbe33b3baf49002acc912917c4ff25d31e\" alt=\"with coordinates x comma y\"></span> for which <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ce672c12451ce6d730167e9763ac3e67a5ed07d54cba747ed2f59adb20d5d205\" alt=\"y equals 0\"></span>. Since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/01dad43d432a687d231ff42df4f77294a187cbda324e65355238edefd6b11057\" alt=\"y equals, h of x\"></span> models the height above the ground, in feet, of the projectile, a <span class=\"italic\">y</span>-value of 0 must correspond to the height of the projectile when it is 0 feet above ground or, in other words, when the projectile is on the ground. Since <span class=\"italic\">x</span> represents the time since the projectile was launched, it follows that the positive <span class=\"italic\">x</span>-intercept, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ac6a13c4378bac2c90332f9964fdca630f3b4512f038cf81d11a87f694f92a0f\" alt=\"the point with coordinates x comma 0\"></span>, represents the time at which the projectile hits the ground.</p><p>Choice A is incorrect and may result from misidentifying the <span class=\"italic\">y</span>-intercept as a positive <span class=\"italic\">x</span>-intercept. Choice B is incorrect and may result from misidentifying the <span class=\"italic\">y</span>-value of the vertex of the graph of the function as an <span class=\"italic\">x</span>-intercept. Choice C is incorrect and may result from misidentifying the <span class=\"italic\">x</span>-value of the vertex of the graph of the function as an <span class=\"italic\">x</span>-intercept.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.615000+00:00","source_updated_at":"2023-08-02T20:25:59.615000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">The initial height of the projectile</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">The maximum height of the projectile</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">The time at which the projectile reaches its maximum height</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">The time at which the projectile hits the ground</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}}