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

Feb 12, 2017

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:

$y = 2 | - 6 + 6 | - 10 \text{ "->" } y = 2 \left(0\right) - 10 = - 10$

Feb 12, 2017

See the Socratic graph and explanation.

#### Explanation:

$y + 10 = 2 | x + 6 | \ge 0$.

So, $y \ge - 10$.

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

V-part above, of the pair of lines

$\left(y - 2 x - 2\right) \left(y + 2 x + 22\right) = 0$

Algebraic proof:

In addition to $y \ge - 10$,

$y + 10 = 2 \left(x + 6\right)$, giving $y - 2 x - 2 = 0$, when $x \ge - 6$ and

$y + 10 = - 2 \left(x + 6\right)$, giving $y + 2 x + 22 = 0$, when $x \le - 6$

The Socratic graph is inserted.

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