Finding Intervals of Increase for Parabola y = -2(x-4)² + 5 with Vertex (4,5)

To solve this problem and find the intervals of increase for the function, let's follow these steps:

• Step 1: Identify the nature of the parabola.
• Step 2: Determine the intervals where the function is increasing.
• Step 3: Provide a clear explanation of the result.

Now, let's dive into each step:
Step 1: We know the quadratic function opens downwards because the coefficient of $x^2$ is $-2$, which is negative. This implies that the vertex is at a maximum point, and the parabola decreases on either side of the vertex.

Step 2: The vertex given is $(4, 5)$. For parabolas that open downwards, the function is increasing to the left of the vertex. Therefore, the function is increasing for $x < 4$.

Step 3: Therefore, the interval of increase for the parabola is $x < 4$.

In conclusion, the interval where the function is increasing is $x < 4$.