Answer
Domain: The set of all real numbers.
Range: $(-\infty , 15 ]$
Work Step by Step
Given $$\begin{aligned}
f(x) &= -2(x+4)^2 +15.
\end{aligned}$$ Compare the given parabola with the standard vertex form:
$$ f(x) = a(x-h)^2+k.$$ We see that this parabola opens downward since the constant, $a= -2$. The maximum value is $k= 15$. The domain and range of the function are given below.
Domain: The set of all real numbers.
Range: $(-\infty , 15 ]$
