Answer:
The graph not have x-intercepts
Step-by-step explanation:
we know that
The x-intercept is the value of x when the value of y is equal to zero
we have
[tex]y=\left|x-2\right|+12[/tex]
This is the equation of an absolute value in vertex form open upward
The vertex is the point (2,12)
The y-coordinate of the vertex is above the x-axis and the graph open upward
That means ----> The graph do not intersect the x-axis
therefore
The graph not have x-intercepts
Verify
For y=0
substitute in the equation
[tex]0=\left|x-2\right|+12[/tex]
[tex]\left|x-2\right|=-12[/tex] ----> is not true
The left side of the equation cannot be a negative number
so
The equation not have solution for y=0
therefore
The graph not have x-intercepts
see the attached figure to better understand the problem
