Find Decreasing Intervals for the Quadratic Function y = x² + 10x + 16

To solve the problem of finding where the function $y = x^2 + 10x + 16$ is decreasing, we follow these steps:

• Step 1: Compute the derivative of the function.
• Step 2: Set the derivative less than zero to find the critical points where the function is decreasing.
• Step 3: Solve the inequality and interpret the solution.

First, compute the derivative of $y$.
The function is $y = x^2 + 10x + 16$.
The derivative $\frac{dy}{dx}$ is given by: $\frac{dy}{dx} = 2x + 10$

Next, we determine where the derivative is less than zero, indicating a decrease in the function: $2x + 10 < 0$

Solving the inequality:
Subtract 10 from both sides: $2x < -10$
Divide both sides by 2 to isolate $x$: $x < -5$

This solution suggests that the function is decreasing on the interval $x < -5$.

Therefore, the interval where the function $y = x^2 + 10x + 16$ is decreasing is $x < -5$.