Finding Intervals of Increase and Decrease for y = -(x - 4/9)² + 1

To determine the intervals of increase and decrease for the function $y = -\left(x-\frac{4}{9}\right)^2 + 1$, we follow these steps:

• Identify Vertex: The function is in vertex form $y = a(x-h)^2 + k$, where the vertex is at $\left(\frac{4}{9}, 1 \right)$.
• Parabola Direction: Since $a = -1$, which is negative, the parabola opens downwards.
• Interval Analysis:
  • The function is increasing on the interval $x < \frac{4}{9}$, moving left towards the vertex.
  • The function is decreasing on the interval $x > \frac{4}{9}$, moving right away from the vertex.

Therefore, after analyzing the function's behavior, we find that:

The function is increasing on $x < \frac{4}{9}$ and decreasing on $x > \frac{4}{9}$.

Thus, the correct intervals of increase and decrease are:

$\searrow:x>\frac{4}{9}\\\nearrow:x<\frac{4}{9}$