Question

How do you graph `y = -abs(x + 4)`?

Answer 1

This is an upside-down V shape with arms having slope `+-1` and vertex at `(-4, 0)`

Explanation:

`abs(x+4) = x+4` when `x+4 >= 0`, that is when `x >= -4`
So `y = -abs(x+4) = -x-4` has slope `-1` when `x >= -4`

`abs(x+4) = -(x+4)` when `x+4 < 0`, that is when `x < -4`
So `y = -abs(x+4) = x+4` has slope `1` when `x < -4`

The vertex is at the point where `(x+4) = 0`, giving `x = -4` and `y = 0`. So the vertex is at `(-4, 0)`

The intersection with the `y` axis will be where `x=0`. Substituting `x=0` into the equation, we get `y = -abs(4) = -4`. So the intersection is at `(0, -4)`

graph{-abs(x+4) [-13.38, 6.62, -5.84, 4.16]}