Answer
$(-\frac{7}{3},0)$, $(-\frac{5}{3},0)$, $(0,5)$.
Work Step by Step
1. Given $h(x)=3|x+2|-1$, to find the x-intercepts, let $y=0$, we have $3|x+2|-1=0 \Longrightarrow x+2=\pm\frac{1}{3} \Longrightarrow x=-\frac{7}{3}, -\frac{5}{3} $
2. To find the y-intercept, let $x=0$, we have $h(0)=3|0+2|-1=5$.
3. Thus the intercepts are $(-\frac{7}{3},0)$, $(-\frac{5}{3},0)$, $(0,5)$.
