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SAT官方每日一题2011.8.20

信息来源:网络  发布时间:2011-08-24

  SAT官方每日一题之数学---选择:

  Mathematics > Standard Multiple Choice

  Read the following SAT test question and then click on a button to select your answer.

  

math image

 

  The quadratic functionfis graphed in thex y-plane above. If function f of x is less than or equal to ufor all values ofx, which of the following could be the coordinates of pointP?

  Answer Choices

  (A)(2 comma 3.5)

 

  (B)(2.25 comma 3.25)

 

  (C)(2.5 comma 3)

 

  (D)(2.75 comma 4)

 

  (E)(3 comma 2.5)

 

 

 

 

  The correct answer is C

  Explanation

  The fact thatfunction f of x less than or equal to ufor all values ofxmeans that the pointP (t comma u)is the maximum of the quadratic functionf, soP (t comma u)must be the vertex of the parabola. The parabola intersects thex-axis at the points(1 comma 0)and(4 comma 0), sotmust be halfway between1and4. Therefore,t = 1 + ((4 - 1) over 2) = 2.5. Of the choices, the only one withx-coordinate equal to2.5is(2.5 comma 3). Therefore,(2.5 comma 3)could be the coordinates of pointP. 

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