{"id":"cb_question_bank:a4216e8c-4a07-4c83-aa79-3f2994598e7e","source_id":"cb_question_bank","source_item_id":"a4216e8c-4a07-4c83-aa79-3f2994598e7e","external_id":"ccdb450a-31b3-42ec-9532-4859dd3972c3","ibn":null,"question_id":"c7a187a7","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"f left parenthesis x right parenthesis equals x squared minus 18 x minus 360 If the given function f is graphed in the xy -plane, where y equals f left parenthesis x right parenthesis , what is an x -intercept of the graph?","stimulus":"","stimulus_html":null,"stem_html":"

fx=\n\t\n\t\tx\n\t\t2\n\t\n\t-\n\t\n\t\t18\n\t\tx\n\t\n\t-\n\t360\n\n

\n

If the given function f\n is graphed in the xy-plane, where y=fx, what is an x-intercept of the graph?

","rationale_html":"

Choice A is correct. It's given that y=fx. The x-intercepts of a graph in the xy-plane are the points where \n\ty\n\t=\n\t0\n\n. Thus, for an x-intercept of the graph of function f\n, 0=fx. Substituting 0\n for fx in the equation fx=x2-18x-360 yields \n\t0\n\t=\n\t\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\t-\n\t\t\n\t\t\t18\n\t\t\tx\n\t\t\n\t\t-\n\t\t360\n\t\n\n. Factoring the right-hand side of this equation yields 0=x+12x-30. By the zero product property, \n\t\n\t\tx\n\t\t+\n\t\t12\n\t\n\t=\n\t0\n\n and \n\t\n\t\tx\n\t\t-\n\t\t30\n\t\n\t=\n\t0\n\n. Subtracting 12\n from both sides of the equation \n\t\n\t\tx\n\t\t+\n\t\t12\n\t\n\t=\n\t0\n\n yields \n\tx\n\t=\n\t-12\n\n. Adding 30\n to both sides of the equation \n\t\n\t\tx\n\t\t-\n\t\t30\n\t\n\t=\n\t0\n\n yields \n\tx\n\t=\n\t30\n\n. Therefore, the x-intercepts of the graph of y=fx are -12,0 and 30,0. Of these two x-intercepts, only -12,0 is given as a choice.

\n

Choice B is incorrect and may result from conceptual or calculation errors.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.828000+00:00","source_updated_at":"2023-08-02T20:25:59.828000+00:00","options":[{"label":"A","content_html":"

-12,0

","ord":0},{"label":"B","content_html":"

-30,0

","ord":1},{"label":"C","content_html":"

-360,0

","ord":2},{"label":"D","content_html":"

12,0

","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}}