# How do you graph and find the vertex for  y=2abs(x-4)+ 1?

Jul 11, 2015

The vertex is at ($4 , 1$).

#### Explanation:

The standard form for an absolute value equation is

$y = a | x - h | + k$

y = 2|x−4| + 1

So

$a = 2$, $h = 4$, and $k = 1$

Vertex

The vertex is at x = –h = 4.

The $y$-coordinate of the vertex is at $y = k = 1$.

The vertex is at ($4 , 1$).

Graph

Now we prepare a table of $x$ and $y$ values.

The axis of symmetry passes through $x = 4$.

Let's prepare a table with points that are 5 units on either side of the axis, that is, from $x = - 1$ to $x = 9$.

Plot these points.

graph{2|x-4|+1 [-1, 10, -1, 10]}

And we have our graph.