Answer
$(-\frac{7}{3},0),(-\frac{5}{3},0)$, $(0,5)$
Work Step by Step
Step 1. Find the x-intercept(s) by letting $h(x)=0$, we have $3|x+2|-1=0\longrightarrow |x+2|=\frac{1}{3}\longrightarrow x=-2\pm\frac{1}{3}$. Thus $x=-\frac{7}{3},-\frac{5}{3}$ or $(-\frac{7}{3},0),(-\frac{5}{3},0)$
Step 2. Find the y-intercept by letting $x=0$, we have $h(0)=5$ or $(0,5)$
