SAT Math Multiple Choice Question 419: Answer and Explanation

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Test Information

Question: 419

14.

If a quadratic equation is used to model the data shown in the scatterplot above, and the model fits the data exactly, which of the following is a solution to the quadratic equation?

  • A. 28
  • B. 32
  • C. 34
  • D. 36

Correct Answer: B

Explanation:

B

Difficulty: Hard

Category: Problem Solving and Data Analysis / Scatterplots

Strategic Advice: This question requires a conceptual understanding of modeling data and properties of quadratic equations. You also need to recall that a solution to an equation is the same as the x-intercept of the equation's graph.

Getting to the Answer: The graph of a quadratic equation is symmetric with respect to its axis of symmetry. The axis of symmetry occurs at the x-value of the vertex, which according to the graph is 20. You can also see from the graph that one of the x-intercepts is x = 8. This means that 8 is a solution to the quadratic equation. Unfortunately, 8 isn't one of the answer choices. However, because the graph of a quadratic equation is symmetric, the other solution (x-intercept) must be the same distance from the vertex as 8 is, which is 20 - 8 = 12 units. Therefore, the other solution to the equation is x = 20 + 12 = 32.

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