SAT Math Multiple Choice Question 687: Answer and Explanation

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Question: 687

12. Images

A portion of the graph of the quadratic function y = f(x) is shown in the xy-plane above. The function g is defined by the equation g(x) = f(x) + b. If the equation g(x) = 0 has exactly one solution, what is the value of b?

  • A. -2
  • B. -1
  • C. 1
  • D. 2

Correct Answer: D



Advanced Mathematics (transformations) HARD

The graph of y = g(x) = f(x) + b is the graph of f vertically shifted up by b units. If g(x) = 0 has exactly one solution, the graph of y = g(x) can touch the x-axis at only one point: the vertex. Since the vertex of f has a y-coordinate of -2, this can only happen if f is shifted up 2 units, so b = 2.

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