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( )=( - )( + ) Choice D is correct. It’s given that f x x 10 x 13 , which can be rewritten ( )= 2+ - 2 as f x x 3x 130. Since the coefficient of the x -term is positive, the = ( ) graph of y f x in the xy-plane opens upward and reaches its minimum value at ( ) its vertex. The x-coordinate of the vertex is the value of x such that f x reaches ( )= 2+ + its minimum. For an equation in the form f x ax bx c, where a, b, and c -b are constants, the x-coordinate of the vertex is . For the equation 2a ( )= 2+ - = = =- f x x 3x 130, a 1, b 3, and c 130. It follows that the x-coordinate of - 3 -3 ( ) the vertex is (), or . Therefore, f x reaches its minimum when the value of 21 2 -3 x is . 2 Alternate approach: The value of x for the vertex of a parabola is the x-value of the midpoint between the two x-intercepts of the parabola. Since it’s given that ( )=( - )( + ) = ( ) f x x 10 x 13 , it follows that the two x-intercepts of the graph of y f x = =- ( ) in the xy-plane occur when x 10 and x 13, or at the points 10, 0 and (- 13, 0 ) . The midpoint between two points, ( x , y ) and ( x , y ) , is ( x1 + x2, y1 + y2 ) . 1 1 2 2 2 2 Therefore, the midpoint between ( 10, 0 ) and (- 13, 0 ) is ç ççè æ 10 +(- 13 ) , 0 + 0÷ ÷÷ø ö , or 2 2 ( -3 ) ( ) -3 , 0. It follows that f x reaches its minimum when the value of x is . 2 2 49 SAT PRACTICE TEST #4 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS nnn MATH: MODULE 2 Choice A is incorrect. This is the y-coordinate of the y-intercept of the graph of = ( ) y f x in the xy-plane. Choice B is incorrect. This is one of the x-coordinates = ( ) of the x-intercepts of the graph of y f x in the xy-plane. Choice C is incorrect and may result from conceptual or calculation errors.