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What is the vertex of the parabola represented by y = x^2 - 4x + 3?

Practice Questions

Q1
What is the vertex of the parabola represented by y = x^2 - 4x + 3?
  1. (2, -1)
  2. (2, 1)
  3. (1, 2)
  4. (3, 0)

Questions & Step-by-Step Solutions

What is the vertex of the parabola represented by y = x^2 - 4x + 3?
  • Step 1: Identify the coefficients from the equation y = x^2 - 4x + 3. Here, a = 1 and b = -4.
  • Step 2: Use the formula to find the x-coordinate of the vertex: x = -b / (2a).
  • Step 3: Substitute the values of a and b into the formula: x = -(-4) / (2 * 1).
  • Step 4: Simplify the equation: x = 4 / 2 = 2.
  • Step 5: Now that we have the x-coordinate (2), plug it back into the original equation to find the y-coordinate: y = (2)^2 - 4(2) + 3.
  • Step 6: Calculate y: y = 4 - 8 + 3 = -1.
  • Step 7: The vertex of the parabola is (2, -1).
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