SAT Math Multiple Choice Question 463: Answer and Explanation

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Question: 463

x 1 2 3 4 5 6
f(x) 3.5 0 –2.5 –4 –4.5 –4

13. The table above shows several points through which the graph of a quadratic function f(x) passes. One of the x-intercepts for the graph is given in the table. What is the other x-intercept for the graph?

  • A. (–2, 0)
  • B. (5, 0)
  • C. (8, 0)
  • D. (10, 0)

Correct Answer: C



Difficulty: Medium

Category: Passport to Advanced Math / Quadratics

Strategic Advice: This question is much simpler than it looks. Don't waste time trying to find the equation of the quadratic. Rather, think about properties of parabolas, in particular, symmetry.

Getting to the Answer: The graph of a parabola is symmetric with respect to its axis of symmetry (the imaginary vertical line that passes through the x-coordinate of the vertex). This means that each x-intercept must be the same distance from the vertex. Take a careful look at the values in the table. The y-values start at 3.5, decrease to a minimum value of –4.5, and then turn around. The points on each side of the minimum have the same y-values (–4), which means you've found the vertex, (5, –4.5). The x-intercept given in the table is (2, 0), which is 3 horizontal units to the left of 5. Therefore, the other x-intercept must be 3 horizontal units to the right of 5, which is (8, 0).

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