When the quadratic function f is graphed in the xy -plane, where y = f x , its vertex is

Question

When the quadratic function f is graphed in the xy -plane, where y = f x , its vertex is - 3 , 6 . One of the x -intercepts of this graph is - 17 4 , 0 . What is the other x -intercept of the graph?

Accepted Answer

Choice B is correct. Since the line of symmetry for the graph of a quadratic function contains the vertex of the graph, the x -coordinate of the vertex of the graph of y = f x is the x -coordinate of the midpoint of its two x -intercepts. The midpoint of two points with x -coordinates x 1 and x 2 has x -coordinate x m , where x m = x 1 + x 2 2 . It&prime;s given that the vertex is - 3 , 6 and one of the x -intercepts is - 17 4 , 0 . Substituting - 3 for x m and - 17 4 for x 1 in the equation x m = x 1 + x 2 2 yields - 3 = - 17 4 + x 2 2 . Multiplying each side of this equation by 2 yields - 6 = - 17 4 + x 2 . Adding 17 4 to each side of this equation yields - 7 4 = x 2 . Therefore, the other x -intercept is - 7 4 , 0 . Choice A 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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