SAT Math Multiple Choice Question 933: Answer and Explanation

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Question: 933

1. The graph of y = ax2 + bx + c passes through the points (1, –8), (2, –1), (3, 4), and (5, 8). If the maximum valueof y occurs at x = 5, through which other point must the graph of y pass?

  • A. (4, 6)
  • B. (6, 4)
  • C. (8, –1)
  • D. (10, –8)

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Passport to Advanced Math / Quadratics

Strategic Advice: The graph of every quadratic equation is a parabola (a symmetric U-shape), and its maximum (or minimum) value occurs at the x-coordinate of its vertex.

Getting to the Answer: Examine the points that are given-they increase from left to right. You also know that the maximum y-value (the highest point on the graph) occurs at x = 5, which means the vertex of the parabola is (5, 8). This tells you that the points will begin to decrease immediately to the right of that point. Using symmetry, you can find the point that corresponds to each of the given points. The first point, (1, -8), is 4 units to the left of the vertex (5 - 1 = 4), so the point that is 4 units to the right of the vertex (x = 5 + 4) will have the same y-coordinate-the graph must pass through (9, -8). This means you can eliminate D. The second point, (2, -1), is 3 units to the left of the vertex, so the point that is 3 units to the right of the vertex is (8, -1). This means (C) is correct.

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