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一道SAT数学题(抛物线)

  下面是一道关于抛物线的SAT数学题及其解法的内容,非常详细。SAT题中,抛物线是必考的一类,虽然中学课程都有所涉及,还是相对比较抽象,尤其是在理解SAT数学题的表达方式上。下面我们来看看这道关于抛物线的SAT数学题吧。

       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.

  以上就是这道SAT数学题的全部内容,后面附有详细的解析。大家在备考SAT数学题相关内容的时候,可以按照这道SAT数学题的解题思路进行思考,这样就可以更加贴近SAT考试的出题方式,更容易获得高分成绩了。

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