## Algebra: A Combined Approach (4th Edition)

Vertex=$(-1,3)$ 1st x-intercept=$(-7,0)$ 2nd x-intercept=$(5,0)$
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.