{"id":"cb_question_bank:5361a02e-9b23-4251-93b8-5cc489b48d48","source_id":"cb_question_bank","source_item_id":"5361a02e-9b23-4251-93b8-5cc489b48d48","external_id":null,"ibn":"070621-DC","question_id":"97e50fa2","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of equations in two variables","difficulty":"H","score_band":6,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The graph of the function f , defined by f of x equals, negative one-half times, open parenthesis, x minus 4, close parenthesis, squared, plus 10 , is shown in the xy -plane above. If the function g (not shown) is defined by g of x equals, negative x plus 10 , what is one possible value of a such that f of a equals, g of a ?","stimulus":"The figure presents the graph of a curve in the xy-plane. The curve is labeled y equals f of x. The numbers 0 through 9 are indicated on the x-axis. The numbers 0 through 12, in increments of 2, are indicated on the y-axis. The curve begins at the point with coordinates 0 comma 2 and moves upward and to the right reaching a maximum at the point with coordinates 4 comma 10. It turns and moves downward and to the right, ending at 8 point 5 on the x-axis","stimulus_html":"
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The graph of the function f, defined by \"f, is shown in the xy-plane above. If the function g (not shown) is defined by \"g, what is one possible value of a such that \"f ?

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The correct answer is either 2 or 8. Substituting \"x in the definitions for f and g gives \"f and \"g, respectively. If \"f, then \"negative. Subtracting 10 from both sides of this equation gives \"negative. Multiplying both sides by \"negative gives \"open. Expanding \"open gives \"a,. Combining the like terms on one side of the equation gives \"a,. One way to solve this equation is to factor \"a, by identifying two numbers with a sum of \"negative and a product of 16. These numbers are \"negative and \"negative, so the quadratic equation can be factored as \"open. Therefore, the possible values of a are either 2 or 8. Note that 2 and 8 are examples of ways to enter a correct answer.

Alternate approach: Graphically, the condition \"f implies the graphs of the functions \"y and \"y intersect at \"x. The graph \"y is given, and the graph of \"y may be sketched as a line with y-intercept 10 and a slope of \"negative (taking care to note the different scales on each axis). These two graphs intersect at \"x and \"x.

\n","correct_answer":["2","8"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.631000+00:00","source_updated_at":"2023-08-02T20:25:59.631000+00:00","options":[],"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}}