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What is the vertex of the parabola defined by the equation y = -2(x - 1)^2 + 4?

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Question: What is the vertex of the parabola defined by the equation y = -2(x - 1)^2 + 4?

Options:

  1. (1, 4)
  2. (1, -4)
  3. (4, 1)
  4. (-1, 4)

Correct Answer: (1, 4)

Solution: 

The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).

What is the vertex of the parabola defined by the equation y = -2(x - 1)^2 + 4?

Practice Questions

Q1
What is the vertex of the parabola defined by the equation y = -2(x - 1)^2 + 4?
  1. (1, 4)
  2. (1, -4)
  3. (4, 1)
  4. (-1, 4)

Questions & Step-by-Step Solutions

What is the vertex of the parabola defined by the equation y = -2(x - 1)^2 + 4?
  • Step 1: Identify the equation of the parabola, which is y = -2(x - 1)^2 + 4.
  • Step 2: Recognize that this equation is in the vertex form, which is y = a(x - h)^2 + k.
  • Step 3: In the vertex form, 'h' is the x-coordinate of the vertex and 'k' is the y-coordinate of the vertex.
  • Step 4: From the equation, we see that h = 1 (because of (x - 1)) and k = 4 (the constant term).
  • Step 5: Combine h and k to find the vertex, which is (h, k) = (1, 4).
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