每日一题

Mathematics>Standard Multiple Choice

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

The quadratic function f is graphed in the x y-plane above. If function f(x) is less than or equal to u for all values of x, which of the following could be the coordinates of point P?

(A) (2，3.5)
(B) (2.25，3.25)
(C) (2.5，3)
(D) (2.75，4)
(E) (3，2.5)

答案和解析

答案：C

解析：

The fact that function f of x less than or equal to u for all values of x means that the point P (t，u) is the maximum of the quadratic function f, so P (t，u) must be the vertex of the parabola. The parabola intersects the x-axis at the points (1，0) and (4，0), so t must be halfway between 1 and 4. Therefore, t = 1 + ((4 minus 1) over 2) = 2.5. Of the choices, the only one with x-coordinate equal to 2.5 is (2.5，3). Therefore, (2.5，3) could be the coordinates of point P.