Question

How do you graph `y = -abs(x+6)`?

Answer 1

This is an upside-down V shape with arms having slope `+-1` and vertex at `(-6, 0)`

Explanation:

`abs(x+6) = x+6` when `x+6 >= 0`, that is when `x >= -6`
So `y = -abs(x+6) = -x-6` has slope `-1` when `x >= -6`

`abs(x+6) = -(x+6)` when `x+6 < 0`, that is when `x < -6`
So `y = -abs(x+6) = x+6` has slope `1` when `x < -6`

The vertex is at the point where `(x+6) = 0`, giving `x = -6` and `y = 0`. So the vertex is at `(-6, 0)`

The intersection with the `y` axis will be where `x=0`. Substituting `x=0` into the equation, we get `y = -abs(6) = -6`. So the intersection is at `(0, -6)`

graph{-abs(x+6) [-13.63, 6.37, -6.96, 3.04]}