SAT Math Multiple Choice Question 629: Answer and Explanation

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Question: 629

14. If m > 1, which of the following could be the graph of y = - (x + m)2 + m in the xy-plane?

  • A.

    Images

  • B.

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  • C.

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  • D.

    Images

Correct Answer: D

Explanation:

D

Algebra (graphs of quadratic equations) HARD

Recall from Chapter 9, Lesson 6, that any equation in the form y = a(x - h)2 + k has a vertex at (h, k) and is open up if a > 0 and down if a < 0. In the equation y = -(x + m)2 + m; therefore, the vertex is (-m, m), and a = -1. Since m > 1, this means that the vertex of the parabola has a negative x-coordinate and a positive y-coordinate, which means the vertex is in quadrant II. And since a < 0, the parabola is open down. The only graph among the choices that is an open down parabola with a vertex in the second quadrant is the graph in choice (D).

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