Answer
Vertex=$(-1,3)$
1st x-intercept=$(-7,0)$
2nd x-intercept=$(5,0)$
Work Step by Step
Our function is $f(x)=-\frac{1}{2}|x+1|+3$
We can write the function in the form $f(x)=a|x-h|+k$
We can conclude that:
$a=-\frac{1}{2}$
$h=-1$
$k=3$
Vertex=$(h,k)=(-1,3)$
To find the x-intercepts we substitute y for 0.
$0=-\frac{1}{2}|x+1|+3$
Then you solve the equation.
Subtract 3 from both sides.
$-3=-\frac{1}{2}|x+1|$
Divide by $-\frac{1}{2}$ on both sides
$6=|x+1|$
Two possibilities:
possibility 1:
$6=x+1$
x=5
possibility 2:
$6=-x-1$
7=-x
x=-7
Therefore the 2 x-intercepts are $(-7,0)$ and $(5,0)$
Graph the vertex and the two x-intercepts on a graph and connect the x-intercepts with the vertex.