Question

How do you graph `y=2abs(x+6)-10`?

Answer 1

See the explanation

Explanation:

The bit inside the | | can be positive or negative but writing it like `|x+6|` always turns the answer to that part into being positive. As a graph it becomes:

At `x-6` we have:

`y=2|-6+6|-10" "->" "y=2(0)-10 = -10`

Answer 2

See the Socratic graph and explanation.

Explanation:

`y+10=2|x+6|>=0`.

So, `y>=-10`.

The equation represents the point of intersection #V(-6, -10) and the

V-part above, of the pair of lines

`(y-2x-2)(y+2x+22)=0`

Algebraic proof:

In addition to `y >= -10`,

`y+10=2(x+6)`, giving `y-2x-2=0`, when `x >=-6` and

`y+10=-2(x+6)`, giving `y+2x+22=0`, when `x<=-6`

The Socratic graph is inserted.

graph{2|x+6|-10 [-20, 20, -11, 9]}