f x = 4 x 2 - 50 x + 126 The given equation defines the function f . For

Question

f x = 4 x 2 - 50 x + 126 The given equation defines the function f . For what value of x does f x reach its minimum?

Accepted Answer

The correct answer is 25 4 . The given equation can be rewritten in the form f x = a x - h 2 + k , where a , h , and k are constants. When a > 0 , h is the value of x for which f x reaches its minimum. The given equation can be rewritten as f x = 4 x 2 - 50 4 x + 126 , which is equivalent to f x = 4 x 2 - 50 4 x + 50 8 2 - 50 8 2 + 126 . This equation can be rewritten as f x = 4 x - 50 8 2 - 50 8 2 + 126 , or f x = 4 x - 50 8 2 - 4 50 8 2 + 126 , which is equivalent to f x = 4 x - 25 4 2 - 121 4 . Therefore, h = 25 4 , so the value of x for which f x reaches its minimum is 25 4 . Note that 25/4 and 6.25 are examples of ways to enter a correct answer.

Question f-x-4-