Answer
See graph,
vertex $(-4,-5)$, axis $x=-4$,
x-intercepts $(-4\pm\frac{\sqrt {15}}{3},0)$, y-intercept $(0,43)$,
domain $(-\infty,\infty)$, range $[-5,\infty)$, increasing $(-4,\infty)$, decreasing $(-\infty,-4)$.
Work Step by Step
Step 1. Graph the function $f(x)=3(x+4)^2-5$ as shown in the figure.
Step 2. We can identify the vertex $(-4,-5)$, axis $x=-4$,
Step 3. For x-intercepts, let $f(x)=0$, we have $3(x+4)^2-5=0$ and $x=-4\pm\frac{\sqrt {15}}{3}$ or $(-4\pm\frac{\sqrt {15}}{3},0)$. For y-intercept, we have $f(0)=43$ or $(0,43)$,
Step 4. We can find domain $(-\infty,\infty)$, range $[-5,\infty)$, and largest open intervals of the domain over which each function is increasing $(-4,\infty)$, decreasing $(-\infty,-4)$.
