Answer
$f(x) = -3|x-1|+5$
Vertex= (1,5)
x-intercept: $(-\frac{2}{3},0),(\frac{8}{3},0)$
y-intercept: (0,2)
Work Step by Step
$f(x) = -3|x-1|+5$
The graph is y=|x| with a dilation of factor $3$ from the x axis, a reflection in the x-axis, and a translation of 1 unit in the positive x direction and 5 units in the positive y direction. Thus, the vertex is (1,5).
To find the x-intercept, we substitute in y=0.
$0 = -3\times|x-1|+5$
$3\times|x-1| = 5$
$|x-1| = \frac{5}{3}$
$x-1=\frac{5}{3}, and -x+1=\frac{5}{3}$
$x=\frac{8}{3}, x=-\frac{2}{3}$
Therefore, the x-intercepts are $(-\frac{2}{3},0),(\frac{8}{3},0)$
To find the y-intercept, we substitute in x=0.
$y = -3\times1+5=2$
Therefore, the y-intercept is (0,2).