sat-dog

= + =4 2+64 +262 Choice A is correct. It’s given that g^xh f^x 5h. Since f^xh x x , it +5 =4 +5 2+64 +5 +262 +5 2 follows that f^x h ^x h ^x h . Expanding the quantity ^x h +5 =4 2+10 +25 +64 +5 +262 in this equation yields f^x h ^x x h ^x h . Distributing 64 +5 =4 2+40 +100+64 +320+262 the 4 and the yields f^x h x x x . Combining +5 =4 2+104 +682 =4 2+104 +682 like terms yields f^x h x x . Therefore, g^xh x x . = - 2+ For a quadratic function defined by an equation of the form g^xh a^x hh k, where a, h, and k are constants and a is positive, g^xh reaches its minimum, k, 37 SAT PRACTICE TEST #9 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1 =4 2+104 +682 when the value of x is h. The equation g^xh x x can be rewritten in this form by completing the square. This equation is equivalent to =4 2+26 +682 =4 2+26 +169-169 +682 g^xh ^x xh , or g^xh ^x x h . This =4 +13 2-169 +682 equation can be rewritten as g^xh ^^x h h , or =4 +13 2-4 169 +682 =4 +13 2+6 g^xh ^x h ^ h , which is equivalent to g^xh ^x h . = - 2+ = =-13 = This equation is in the form g^xh a^x hh k, where a 4, h , and k 6. -13 Therefore, g^xh reaches its minimum when the value of x is . Choice B is incorrect. This is the value of x for which f^xh, rather than g^xh, reaches its minimum. Choice C is incorrect and may result from conceptual or - calculation errors. Choice D is incorrect. This is the value of x for which f^x 5h, + rather than f^x 5h, reaches its minimum.