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14 Aug 2025, 04:46
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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A graph of the function \(g(x)\) is shown above. \(g(x)\) is defined by which of the following equations?
A. \(g(x)=(x+1)^2-2\)
B. \(g(x)=(x-1)^2-2\)
C. \(g(x)=(x+1)^2+2\)
D. \(g(x)=(x-1)^2+2\)
E. \(g(x)=(x-2)^2+1\)
25 Aug 2025, 00:12
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Official Explanation
The easiest approach is to substitute the xy-coordinate values of points on the curve into the functions given in the answer choices, to see which choice produces the proper y-value for a given x-value. Begin with the vertex, an important point on a parabola, given here by the coordinates (1, -2). If the equation of the parabola is g(x), then g(1) must equal -2. In choice (B), \(g(1) = (1 - 1)^2 - 2 = 0 - 2 = -2.\) No other choice contains a function such that g(1) = -2.
*The function given in choice (B), \(g(x) = (x - 1)^2 - 2,\) represents a transformation of the common function, f(x) = x^2, whose graph in the xy-plane is a parabola pointed upward with vertex at the origin (0, 0,). Replacing x with (x - 1) causes a horizontal translation 1 unit to the right, and subtracting 2 causes a vertical translation 2 units down. Since the graph depicted has been shifted 1 unit to the right and 2 units down from the origin, (B) is correct.
Answer: B
The easiest approach is to substitute the xy-coordinate values of points on the curve into the functions given in the answer choices, to see which choice produces the proper y-value for a given x-value. Begin with the vertex, an important point on a parabola, given here by the coordinates (1, -2). If the equation of the parabola is g(x), then g(1) must equal -2. In choice (B), \(g(1) = (1 - 1)^2 - 2 = 0 - 2 = -2.\) No other choice contains a function such that g(1) = -2.
*The function given in choice (B), \(g(x) = (x - 1)^2 - 2,\) represents a transformation of the common function, f(x) = x^2, whose graph in the xy-plane is a parabola pointed upward with vertex at the origin (0, 0,). Replacing x with (x - 1) causes a horizontal translation 1 unit to the right, and subtracting 2 causes a vertical translation 2 units down. Since the graph depicted has been shifted 1 unit to the right and 2 units down from the origin, (B) is correct.
Answer: B
