Question

What is the location of the vertex for the graph of y≥|x-1|

Answer 1

`(1,0)`

1) We can find algebraically the vertex of that Absolute Value inequality, by doing this procedure:

`\begin{gathered} y\ge|x-1| \\ |x-1|=0 \end{gathered}`

2) Since the vertex is where the absolute value is equal to zero, let's solve as an equation, and then treat it back as an inequality to write the answer:

`\begin{gathered} |x-1|=0 \\ x=1 \\ --- \end{gathered}`

Now let's plug the quantity of "x" we just found to find the y-coordinate:

`\begin{gathered} y=|x-1| \\ y=|1-1| \\ y=|0| \\ y=0 \end{gathered}`

So the answer is:

`(1,0)`