Question

How do you graph `y - 2 = - | x + 3 | + 1`?

Answer 1

It helps to list the transformations. But it's not necessary; you can sub in values and solve for the other value. Plot those values.

Explanation:

First off, let's add a `2` to the equation in order to isolate `y`.

Now we have:`y= - | x + 3 | + 3`

Before we graph, let's list the transformations.

• Reflection in the `x`-axis.
• Vertical translation `3` units up.
• Horizontal translations `3` units left.

Now we know what to expect. So, let's sub in values of `x` and solve for `y`.

Then, we plot the values of `x` and `y`.

We should get this:

graph{y= - | x + 3 | + 3 [-10, 10, -5, 5]}

Hope this helps :)