Find Intervals of Increase and Decrease for y = (x - 2⅑)² + 5/6

To solve the problem, let's first identify the form and properties of the given function: $y = (x - 2\frac{1}{9})^2 + \frac{5}{6}$.

The function is a quadratic in vertex form, $y = (x - h)^2 + k$, where $h = 2\frac{1}{9}$ and $k = \frac{5}{6}$. In this form, the vertex is at $x = 2\frac{1}{9}$. The coefficient of the squared term is positive, indicating that the parabola opens upwards.

The vertex point $(2\frac{1}{9}, \frac{5}{6})$ is the minimum point of the parabola. For a quadratic function opening upwards:

• The function decreases when $x < 2\frac{1}{9}$.
• The function increases when $x > 2\frac{1}{9}$.

Therefore, the intervals of decrease and increase are as follows:
- Decreasing: $x < 2\frac{1}{9}$
- Increasing: $x > 2\frac{1}{9}$

Comparing this with the answer choices, the correct choice is:

$\searrow:x<2\frac{1}{9}\\\nearrow:x>2\frac{1}{9}$