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

Practice Questions

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

Questions & Step-by-Step Solutions

What is the vertex of the parabola represented by the equation y = x^2 - 4x + 4?
  • Step 1: Identify the coefficients in the equation y = x^2 - 4x + 4. Here, a = 1 and b = -4.
  • Step 2: Use the formula for the x-coordinate of the vertex, which is 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 x = 2, substitute this value back into the original equation to find y: y = (2)^2 - 4*(2) + 4.
  • Step 6: Calculate y: y = 4 - 8 + 4 = 0.
  • Step 7: The vertex of the parabola is (2, 0).
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