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 ≤ x ≤ 1 0. Which of the following is the best interpretation of the vertex of the graph of y = f(x) in the xy-plane?
","rationale_html":"Choice A is correct. The graph of a quadratic equation in the form =( -)2 + y a x h k, where a, h, and k are positive constants, is a parabola that ( ) ( )= 1( - )2+ opens upward with vertex h, k. The given functiofn x x 7 3 is in the 9 =( -)2 + = ( ) =1 = = form y a x h k, where y f x , a , h 7, and k 3. Therefore, the = ( ) 9 ( ) 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 ( ) ( ) ( )= 1( - )2+ f x . Therefore, the minimum value of f x is 3. It’s given thaft x x 7 3 9 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.
","correct_answer":["A"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"The metal ball’s minimum height was 3 inches above the ground.
","ord":0},{"label":"B","content_html":"The metal ball’s minimum height was 7 inches above the ground.
","ord":1},{"label":"C","content_html":"The metal ball’s height was 3 inches above the ground when it started moving.
","ord":2},{"label":"D","content_html":"The metal ball’s height was 7 inches above the ground when it started moving.
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