Question

How many x intercepts does the graph of y =|x-2|+12

Answer 1

The graph not have x-intercepts

Explanation:

we know that

The x-intercept is the value of x when the value of y is equal to zero

we have

`y=\left|x-2\right|+12`

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

`0=\left|x-2\right|+12`

`\left|x-2\right|=-12` ----> 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