Find Increasing Intervals for the Quadratic Function y = (x+1)(x+5)

To find the intervals where the function $y = (x+1)(x+5)$ is increasing, we need to analyze its derivative.

We start by expanding the function: $y = (x+1)(x+5) = x^2 + 6x + 5$.

Next, we find the derivative: $y' = \frac{d}{dx}(x^2 + 6x + 5) = 2x + 6$.

To find where the function is increasing, solve the inequality $2x + 6 > 0$:

• Subtract 6 from both sides: $2x > -6$
• Divide by 2: $x > -3$

This tells us that the function is increasing on the interval $x > -3$.

By analyzing the derivative, the function transitions at $x = -3$, from decreasing (when $x < -3$) to increasing (when $x > -3$).

Therefore, the solution is $x > -3$.