The function f x = 1 9 x - 7 2 + 3 gives a metal ball's height above the

Question

The function f x = 1 9 x - 7 2 + 3 gives a metal ball's height above the ground f x , in inches, x seconds after it started moving on a track, where 0 &#8804; x &#8804; 10 . Which of the following is the best interpretation of the vertex of the graph of y = f x in the xy -plane?

Accepted Answer

Choice A is correct. The graph of a quadratic equation in the form y = a x - h 2 + k , where a , h , and k are positive constants, is a parabola that opens upward with vertex h , k . The given function f x = 1 9 x - 7 2 + 3 is in the form y = a x - h 2 + k , where y = f x , a = 1 9 , h = 7 , and k = 3 . Therefore, the graph of y = f x is a parabola that opens upward with vertex 7 , 3 . Since the parabola opens upward, the vertex is the lowest point on the graph. It follows that the y -coordinate of the vertex of the graph of y = f x is the minimum value of f x . Therefore, the minimum value of f x is 3 . It&rsquo;s given that f x = 1 9 x - 7 2 + 3 represents the metal ball&rsquo;s height above the ground, in inches, x seconds after it started moving on a track. Therefore, the best interpretation of the vertex of the graph of y = f x is that the metal ball&rsquo;s minimum height was 3 inches above the ground. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

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