# How do you graph and find the vertex for  y = 4 - abs(x+2) ?

Jun 13, 2015

Take the graph of $\left\mid x \right\mid$, turn it upside down, shift it two to the left, and elevate it vertically by four, making the vertex at $\left(- 2 , 4\right)$.

#### Explanation:

Sometimes it's best to write these equations in a slightly different way, to see it. Here, $y$ can be rewritten:

$y = - \left\mid x + 2 \right\mid + 4$

From there it also helps to know what the graph of $y = \left\mid x \right\mid$ looks like:

graph{y=abs(x)}

Notice it's just the graph of $y = x$ mashed together with $y = - x$. And like you would expect with $\left\mid x \right\mid$, there are no negative $y$ values. And if we graph the negative, $y = - \left\mid x \right\mid$, we turn it upside down, like so:

graph{y=-abs(x)}

Adding 2 to the inside of the absolute value shifts the vertex (perhaps counter-intuitively) to the left by 2 units, like so:

graph{y=-abs(x+2)}

Finally, adding 4 to the end of our new graph, shifts the vertex 4 units vertically, creating the following:

graph{y=-abs(x+2)+4}

Finis!