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Which of the following is the correct vertex form of the quadratic equation y =

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Question: Which of the following is the correct vertex form of the quadratic equation y = x² - 4x + 3?

Options:

  1. y = (x - 2)² - 1
  2. y = (x + 2)² - 1
  3. y = (x - 2)² + 1
  4. y = (x + 2)² + 1

Correct Answer: y = (x - 2)² - 1

Solution: 

Completing the square for the equation y = x² - 4x + 3 results in y = (x - 2)² - 1.

Which of the following is the correct vertex form of the quadratic equation y =

Practice Questions

Q1
Which of the following is the correct vertex form of the quadratic equation y = x² - 4x + 3?
  1. y = (x - 2)² - 1
  2. y = (x + 2)² - 1
  3. y = (x - 2)² + 1
  4. y = (x + 2)² + 1

Questions & Step-by-Step Solutions

Which of the following is the correct vertex form of the quadratic equation y = x² - 4x + 3?
  • Step 1: Start with the original equation: y = x² - 4x + 3.
  • Step 2: Identify the coefficient of x, which is -4. To complete the square, take half of -4, which is -2.
  • Step 3: Square -2 to get 4. This is the number we will add and subtract in the equation.
  • Step 4: Rewrite the equation by adding and subtracting 4: y = (x² - 4x + 4) - 4 + 3.
  • Step 5: Simplify the equation: y = (x - 2)² - 1.
  • Step 6: The equation is now in vertex form: y = (x - 2)² - 1.
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