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

To find the domain of increase for the function $y = -x^2 + 2x + 35$, let's determine the vertex first.

• Step 1: Identify coefficients in the quadratic equation. Here, $a = -1$, $b = 2$, and $c = 35$.
• Step 2: Use the vertex formula $x = -\frac{b}{2a}$ to find the x-coordinate of the vertex.

Plug in the values for $b$ and $a$:

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

The x-coordinate of the vertex is $x = 1$.

Since the coefficient $a$ is negative, this means the parabola opens downwards. A parabola opening downward will increase until it reaches the vertex, then start decreasing.

Therefore, the domain on which the function is increasing is $x < 1$.

Therefore, the solution to the problem is $x < 1$.