SAT Math Multiple Choice Question 283: Answer and Explanation

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Question: 283


The range of the parabola shown in the graph is y ≥ -4. If the equation y = ax2 + bx + c is used to represent the graph, what is the value of a?

  • A.
  • B.
  • C.
  • D. 3

Correct Answer: A



Difficulty: Hard

Category: Passport to Advanced Math / Quadratics

Strategic Advice: To write the equation of a parabola, you need two things-the vertex and one other point. In this question, you already have a point, but you'll need to reason logically to find the vertex. Use these two facts: The vertex of a parabola lies on its axis of symmetry, and the range of a quadratic equation depends on the y-coordinate of the vertex.

Getting to the Answer: The vertex of the parabola shown must lie on its axis of symmetry, which is halfway between the two points (0, 8) and (12, 8). This means the x-coordinate of the vertex is halfway between 0 and 12, which is 6. To find the y-coordinate of the vertex, look at the range: means that the minimum value of the graph, and hence the y-coordinate of the vertex, is -4. Now, use the vertex (6, -4) to set up a quadratic equation in vertex form: y = a(x - h)2 + k. The result is y = a(x - 6)2 - 4. Plug in either of the given points for x and y to find the value of a. Using (0, 8), the result is:

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