Find Decreasing Intervals for the Quadratic Function y = x² + 4x + 5

To find the intervals where the function is decreasing, follow these steps:

• Step 1: Differentiate the given function: $y = x^2 + 4x + 5$.
• Step 2: The derivative is $y' = 2x + 4$.
• Step 3: Set the derivative less than zero to find decreasing intervals: $2x + 4 < 0$.
• Step 4: Solve $2x + 4 < 0$ for $x$.

Let's perform the calculations:

The derivative of the function is $y' = 2x + 4$.

Set the inequality: $2x + 4 < 0$.
Subtract 4 from both sides: $2x < -4$.
Divide both sides by 2: $x < -2$.

Therefore, the function $y = x^2 + 4x + 5$ is decreasing for $x < -2$.

The correct answer choice is: $x < -2$.