h = -2
To express x² + 4x + 5 in the form a(x - h)² + k, we can complete the square. Following the steps below:
- Start with the equation x² + 4x + 5.
- Rewrite it as x² + 4x and identify the coefficient of x, which is 4.
- Take half of this coefficient (4/2 = 2) and square it to get (2² = 4).
- Add and subtract this square inside the equation: x² + 4x + 4 - 4 + 5.
- Rewrite the equation as: (x + 2)² - 4 + 5.
- 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.
