Answer
g(x) = 3|x| +2
Vertex: (0,2)
x-intercepts: There are none.
y-intercepts: (0,2)
Work Step by Step
g(x) = 3|x| +2
The graph is essentially y=|x| with a dilation of factor 3 from the x-axis and a translation of 2 units in the positive y-direction. As such, the vertex is (0,2).
To find the x-intercepts, we substitute in y=0.
0 = 3|x|+2
3|x| = -2
But since |x|>0, there are no solutions to this equation. Thus, there are no x-intercepts.
Finding the y-intercept by substituting the point x = 0:
y = 0+2 = 2
Therefore, the y-intercept is (0,2).
