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If we express x² + 4x + 5 in the form a(x - h)² + k, then what is h?

Sagot :

h = -2

To express x² + 4x + 5 in the form a(x - h)² + k, we can complete the square. Following the steps below:

  1. Start with the equation x² + 4x + 5.
  2. Rewrite it as x² + 4x and identify the coefficient of x, which is 4.
  3. Take half of this coefficient (4/2 = 2) and square it to get (2² = 4).
  4. Add and subtract this square inside the equation: x² + 4x + 4 - 4 + 5.
  5. Rewrite the equation as: (x + 2)² - 4 + 5.
  6. Simplify to get the final form: (x + 2)² + 1.

The expression is now in the form a(x - h)² + k with h = -2, a = 1 and k = 1.

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