QuestionFor the quadratic function $f(x)=x^{2}+6 x$, answer parts (a) through ( $f$ ). concave up (b) Find the $y$-intercept and the $x$-intercepts, if any.
What is the $y$-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept is 0 . $\square$ (Type an integer or a simplified fraction.) B. There is no y-intercept.
What is the x-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $x$-intercept(s) is/are $0,-6$. $\square$ (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no x-intercepts. (c) Use parts (a) and (b) to graph the function.
Use the graphing tool to graph the function.
Click to enlarge graph (d) Find the domain and the range of the quadratic function.
The domain of $f$ is $(-\infty, \infty)$. (Type your answer in interval notation.) The range of $f$ is $[-9, \infty)$. (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 $(-3, \infty)$. (Type your answer in interval notation.) The function is decreasing on the interval $(-\infty,-3)$. (Type your answer in interval notation.) (f) Determine where $f(x)>0$ and where $f(x)<0$. Select the correct choice below and fill in the answer box(es) within your choice. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) A. $f(x)<0$ on $\square$ , and $f(x)$ is never positive B. $f(x)>0$ on $\square$ , and $f(x)$ is never negative C. $f(x)>0$ on $\square$ , and $\mathrm{f}(\mathrm{x})<0$ on $\square$