Answer
$f(x) = \frac{2}{3}|x+2|-5$
Vertex=(-2,-5)
x-intercept: $(-\frac{19}{2},0), (\frac{11}{2},0)$
y-intercept: $(0,-\frac{11}{3})$
Work Step by Step
$f(x) = \frac{2}{3}|x+2|-5$
The graph is y=|x| with a dilation of factor $\frac{2}{3}$ from the x axis and a translation of 2 units in the negative x direction and 5 units in the negative y direction. Thus, the vertex is (-2,-5).
To find the x-intercept, we substitute in y=0.
$0 = \frac{2}{3}\times|x+2|-5$
$\frac{2}{3}\times|x+2| = 5$
$|x+2| = \frac{15}{2}$
$x+2=\frac{15}{2}, and -x-2=\frac{15}{2}$
$x=\frac{11}{2}, x=-\frac{19}{2}$
Therefore, the x-intercepts are: $(-\frac{19}{2},0), (\frac{11}{2},0)$
To find the y-intercept, we substitute in x=0.
$y = \frac{2}{3}\times2-5=-\frac{11}{3}$
Therefore, the y-intercept is $(0,-\frac{11}{3})$.
