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

1 Answer
Jun 13, 2015

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

Explanation:

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

y=-abs(x+2)+4

From there it also helps to know what the graph of y=abs(x) 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 abs(x), there are no negative y values. And if we graph the negative, y=-abs(x), 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!