Find the Decreasing Domain: Analyzing y = -x² + 2x + 35

To determine the domain over which the quadratic function $y = -x^2 + 2x + 35$ is decreasing, we proceed by identifying the vertex of the parabola.

Given the form $y = ax^2 + bx + c$, we have $a = -1$, $b = 2$, and $c = 35$. The x-coordinate of the vertex can be found using the formula:

$x = -\frac{b}{2a}$

Substituting $b = 2$ and $a = -1$ into the formula, we calculate:

$x = -\frac{2}{2 \times (-1)} = -\frac{2}{-2} = 1$

The vertex of the parabola occurs at $x = 1$. Since the function is a downward-opening parabola (as indicated by the negative coefficient of $-x^2$), the function decreases for all $x$ values greater than the x-coordinate of the vertex.

Therefore, the domain of decrease for the function is $x > 1$.

This matches the answer choice:

$x > 1$