Over what interval is the graph of f (x) = - (x + 8) 2 - 1 decreasing?

F (x) = - (x + 8) ² - 1

The function (not its graph) decreases on interval [-8, ∞). It is a quadratic function in vertex form. That form makes it easy to pick out the one extremum, where x equals - 8. The leading coefficient is negative, so the extremum must be a maximum. The function decreases as x increases from there.

Notice that I include the value - 8 in the interval. The function does not have instantaneous decrease at that value, but that is not what it means for a function to be decreasing over an interval.

Let a and b be any two values on [-8, ∞), such that a < b.

-8 ≤ a < b

Then f (a) > f (b). Therefore, function f is decreasing on interval [-8, ∞).