# How do you graph f(x) =-3abs(x+2)+2?

Sep 21, 2015

#### Explanation:

graph{-3|x+2|+2 [-11.24, 11.26, -5.625, 5.63]}
f(x)=-3|x-2|+2=0
|x-2|=2/3
=>x-2=2/3, -(x-2)=2/3
x=8/3r x=4/3

Sep 21, 2015

You can graph it step by step.

#### Explanation:

Firstly, let's graph the absolute term $| x + 2 |$

When we give values to $x$
$x = - 2$
$| x + 2 | = 0$

$x = 0$
$| x + 2 | = 2$

$x = - 1$
$| x + 2 | = 1$

$x = 1$
$| x + 2 | = 3$

$x = - 3$
$| x + 2 | = 1$

graph{|x + 2| [-4.093, 0.907, -0.41, 2.09]}

You can see that $y$ is always positive and the slope of right part of graph is $1$
Then, we must consider the coefficient of $| x + 2 |$ . The coefficient $\left(- 3\right)$ is going to make the graph narrower and upside down because of negative value. The slope is going to be $\left(- 3\right)$
graph{-3|x+2| [-4.175, 0.825, -2.42, 0.08]}

The final part is adding the last term of function. The term $2$ is going to locate the graph $2$ units upper on ordinate.

$x = 0$
$- 3 | x + 2 | = - 6$

$x = 0$
$- 3 | x + 2 | + 2 = - 4$

Finally, we have:
graph{-3|x+2|+2 [-6.893, 3.107, -2.49, 2.51]}