Question

for the quadratic function f(x)= -x² - 2x, answer parts (a) through (f). the domain of f is (-∞,∞). (type your answer in interval notation.) the range of f is (-∞,1. (type your answer in interval notation.) (e) determine where the quadratic function is increasing and where it is decreasing. the function is increasing on the interval (-∞, -1). (type your answer in interval notation.) the function is decreasing on the interval . (type your answer in interval notation.)

Explanation:

Step1: Recall quadratic - function properties

For a quadratic function $y = ax^{2}+bx + c$, the axis of symmetry is $x=-\frac{b}{2a}$. For $f(x)=-x^{2}-2x$, where $a=-1$ and $b = - 2$, the axis of symmetry is $x=-\frac{-2}{2\times(-1)}=-1$. Since $a=-1\lt0$, the parabola opens down - ward.

Step2: Determine the decreasing interval

The function is increasing to the left of the axis of symmetry and decreasing to the right of the axis of symmetry. So the function $f(x)=-x^{2}-2x$ is decreasing on the interval $(-1,\infty)$.

Answer:

$(-1,\infty)$