Question

How do you graph and find the vertex for `abs y=x`?

Answer 1

The vertex of a function containing a modulus is typically at the point where the enclosed expression changes sign.

In the case of `abs(y) = x` the vertex is at `(0,0)`

When `y >= 0` the equation boils down to `y = x` - the equation of a `45^o` line with slope `1`.

When `y < 0` the equation boils down to `-y = x`, that is `y = -x` - the equation of a line with slope `-1`.

graph{x=abs(y) [-10, 10, -5, 5]}