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

Practice Questions

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

Questions & Step-by-Step Solutions

What is the vertex of the parabola represented by the equation y = x^2 - 4x + 1?
  • Step 1: Identify the coefficients a, b, and c from the equation y = x^2 - 4x + 1. Here, a = 1, b = -4, and c = 1.
  • Step 2: Use the vertex formula x = -b / (2a) to find the x-coordinate of the vertex. Substitute b and a: x = -(-4) / (2 * 1) = 4 / 2 = 2.
  • Step 3: Substitute the x value back into the original equation to find the y-coordinate. Calculate y = (2)^2 - 4(2) + 1.
  • Step 4: Simplify the equation: y = 4 - 8 + 1 = -3.
  • Step 5: Combine the x and y coordinates to find the vertex. The vertex is (2, -3).
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