OG详解-OG4 数学2 Q19

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 they-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’s given that f(x )=1​9​ (x -7)²  +3 represents the metal ball’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’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.