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13 - The correct answer is 2. The value of x for which f^xh reaches its minimum can = - 2+ be found by rewriting the given equation in the form f^xh ^x hh k, where f^xh reaches its minimum, k, when the value of x is h. The given equation, = -2 +15 = 2+13 -30 f^xh ^x h^x h, can be rewritten as f^xh x x . By completing the = 2+13 + 13 2 -30- 13 2 square, this equation can be rewritten as f^xh ax x ` 2 j k ` 2 j , 13 2 289 13 2 289 = + - = - - - which is equivalent to f^xh `x 2 j 4 , or f^xh `x ` 2 jj 4 . Therefore, 13 - f^xh reaches its minimum when the value of x is 2. Note that -13/2 and -6.5 are examples of ways to enter a correct answer. = Alternate approach: The graph of y f^xh in the xy-plane is a parabola. The value of x for the vertex of a parabola is the x-value of the midpoint between the two = -2 +15 x-intercepts of the parabola. Since it’s given that f^xh ^x h^x h, it follows = = that the two x-intercepts of the graph of y f^xh in the xy-plane occur when x 2 =-15 2,0 -15,0 and x , or at the points ^ h and ^ h. The midpoint between two points, ^x 1 , y 1 h and ^x 2 , y 2 h, is c x1+ 2 x2, y1+ 2 y2 m. Therefore, the midpoint between 2,0 -15,0 2-15,0+0 - 13,0 ^ h and ^ h is b 2 2 l, or b 2 l. It follows that f^xh reaches its 13 - minimum when the value of x is 2. Note that -13/2 and -6.5 are examples of ways to enter a correct answer. 38 SAT PRACTICE TEST #7 ANSWER EXPLANATIONS