Find Intervals of Increase and Decrease for y = (x+8)² - 2.25

To solve this problem, we'll determine where the quadratic function $y = (x+8)^2 - 2\frac{1}{4}$ is increasing or decreasing.

This function is in the vertex form: $y = a(x-h)^2 + k$, where $a$ indicates whether the parabola opens upwards ($a > 0$) or downwards ($a < 0$). Here, $a = 1$, indicating the parabola opens upwards.

Let's identify the vertex:

• The vertex form is $(x+8)^2$, thus the vertex $(h, k) = (-8, -2\frac{1}{4})$.

The function is a parabola that opens upwards, so it is decreasing on the left of the vertex and increasing on the right. Specifically:

• Decreasing on the interval $x < -8$.
• Increasing on the interval $x > -8$.

Therefore, the intervals of increase and decrease for the function are:

Decreasing: $x < -8$

Increasing: $x > -8$

Thus, the correct conclusion for the intervals of increase and decrease is:

$\searrow: x < -8 \\ \nearrow: x > -8$