Answer
$f(x) = -2|x-3|+4$
Vertex=(3,4)
x-intercepts: (1,0) and (5,0)
y-intercept: (0,-2)
Work Step by Step
$f(x) = -2|x-3|+4$
The graph is y=|x| with a dilation of factor $2$ from the x axis, a reflection in the x-axis, and a translation of 3 units in the positive x direction and 4 units in the positive y direction. Thus, the vertex is (3,4).
To find the x-intercept, we substitute in y=0.
$0 = -2\times|x-3|+4$
$2\times|x-3| = 4$
$|x-3| = 2$
$x-3=2, and -x+3=2$
$x=5, x=1$
Therefore, the x-intercepts are (5,0) and (1,0).
To find the y-intercept, we substitute in x=0.
$y = -2\times3+4=-2$
Therefore, the y-intercept is (0,-2).