Find Decreasing Intervals of Parabola with Vertex (4,5) and x² Coefficient -2

We know that the equation for the parabola is given in vertex form $f(x) = -2(x-4)^2 + 5$. This form reveals the position of the vertex $(4, 5)$ and the opening direction of the parabola, which opens downward due to the negative coefficient of $-2$.

For a parabola, the intervals of increase and decrease are determined by its symmetry around the vertex. In this case, because the parabola opens downward, it will be increasing on the interval $(-\infty, 4)$ and decreasing on the interval $(4, \infty)$.

The vertex at $x = 4$ is the point where the rate of change (slope) shifts. Thus, to find where the function is decreasing, we look to the right side of the vertex.

Therefore, the function is decreasing for $x > 4$.

In conclusion, the interval where the function is decreasing is $x > 4$.