Answer
See graph,
vertex $(6,7)$, axis $x=6$,
x-intercepts $(6\pm\frac{\sqrt {42}}{2},0)$, y-intercept $(0,-17)$,
domain $(-\infty,\infty)$, range $(-\infty,7]$, increasing $(-\infty,6)$, decreasing $(6,\infty)$.
Work Step by Step
Step 1. Graph the function $f(x)=-\frac{2}{3}(x-6)^2+7$ as shown in the figure.
Step 2. We can identify the vertex $(6,7)$, axis $x=6$,
Step 3. For x-intercepts, let $f(x)=0$, we have $-\frac{2}{3}(x-6)^2+7=0$ thus $x=6\pm\frac{\sqrt {42}}{2}$ or $(6\pm\frac{\sqrt {42}}{2},0)$. For y-intercept, we have $f(0)=-17$ or $(0,-17)$,
Step 4. We can find domain $(-\infty,\infty)$, range $(-\infty,7]$, and largest open intervals of the domain over which each function is increasing $(-\infty,6)$, decreasing $(6,\infty)$.
