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, ∞).

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