SOLUTION: y = |2x - 6| - 2 what is the vertex of this problem when graphed and does the graph open upwards or downwards?

Algebra ->  Absolute-value -> SOLUTION: y = |2x - 6| - 2 what is the vertex of this problem when graphed and does the graph open upwards or downwards?      Log On


   



Question 214873: y = |2x - 6| - 2 what is the vertex of this problem when graphed and does the graph open upwards or downwards?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
+y+=+abs%282x+-+6%29+-+2

To find the vertex:
Set the expression between the absolute value bars
equal to zero, that's just the red part below:

+y+=+abs%28red%282x+-+6%29%29+-+2

red%282x-6%29=0
2x=6
x=3

Now find the y-value that corresponds to that
value of x:

+y+=+abs%282%283%29+-+6%29+-+2
+y+=+abs%286+-+6%29+-+2
+y+=+abs%280%29+-+2
+y+=+0+-+2
+y+=+-2

So the vertex is the point %22%283%2C-2%29%22}

So we plot that point:

 

Now find and plot one point on each side of that point:

So choose x to be 1 less than 3, which is 2, Substitute
in:

+y+=+abs%282x+-+6%29+-+2
+y+=+abs%282%282%29+-+6%29+-+2
+y+=+abs%284+-+6%29+-+2
+y+=+abs%28-2%29+-+2
+y+=+2+-+2
+y+=+0

So we plot the point %22%282%2C0%29%22

 

Next choose x to be 1 more than 3, which is 4, Substitute
in:

+y+=+abs%282x+-+6%29+-+2
+y+=+abs%282%284%29+-+6%29+-+2
+y+=+abs%288+-+6%29+-+2
+y+=+abs%282%29+-+2
+y+=+2+-+2
+y+=+0

So we plot the point %22%284%2C0%29%22



Then we draw the v-shaped graph:



That's it.

Edwin