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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?

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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 comma 3) could be the coordinates of point P.

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