Find Intervals of Increase and Decrease for y = (x - 4.6)² + 2.1

To solve this problem, we need to determine the intervals during which the quadratic function $y = (x - 4.6)^2 + 2.1$ is increasing and decreasing.

• Step 1: Identify the vertex of the parabola from the equation, which is presented in vertex form $y = (x - h)^2 + k$. Here, the vertex is $(4.6, 2.1)$.

• Step 2: Determine the direction of the parabola by examining the sign of the coefficient of the squared term. Since $a = 1$ (positive), the parabola opens upwards.

• Step 3: Identify intervals of increase and decrease:

  • For a parabola opening upwards, the function decreases on the interval $x < 4.6$ and increases on the interval $x > 4.6$.

Therefore, the intervals of increase and decrease for the given function are as follows:
Decreasing: $x < 4.6$
Increasing: $x > 4.6$

This matches choice 2 from the given options, confirming that our analysis was correct.

In conclusion, the solution to the problem is:
$\searrow:x<4.6\\\nearrow:x>4.6$