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 of 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)
The correct answer is C
Explanation
The fact that function f of x less than or equal to u for all values of x means that the point P (t comma u) is the maximum of the quadratic function f, so P (t comma u) must be the vertex of the parabola. The parabola intersects the x-axis at the points (1 comma 0) and (4 comma 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 comma 3). Therefore, (2.5 ,3) could be the coordinates of point P.
