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

1 Answer
Jul 11, 2015

Answer:

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

Explanation:

The standard form for an absolute value equation is

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

Your equation is

#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#.

Table

Plot these points.

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

And we have our graph.