How do you graph #y = | 3x+6|#?

2 Answers
Apr 22, 2016

Answer:

See explanantion

Explanation:

Write out a table for different values of #x#. If the answer is such that y is negative change the answer to positive. That is what the two vertical lines mean. This answer is always positive.

This means that the graph is of general shape #vv#.

#color(blue)("Determine where the slope changes from negative to positive.")#

Write as #y=3|x+2|#

Set y to 0 giving

#0=3|x+2|#

Divide both sides by 3

#0=|x+2|#

#=> x=-2#

So the point of the #color(blue)("vertex" ->(x,y)->(-2,0))#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We only #underline("need two more points")# and you can plot your graph.

I chose one of them to be #x=-3#

So #y=|3(-3)+6|#

#y=|-9+6|#

#y=|-3|#

#y=+3#

#color(blue)("So one point is "(x,y)->(-3,+3))#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I will let you determine the other one.

Tony B

Apr 22, 2016

Answer:

#y>=0#. Draw the straight lines y = 3 x + 6 that passes through #(0, 6) and (-2, 0) and y = -(3 x + 6)# that passes through #(0, -6) and (-2, 0)#. Graph is V-like half of the pair, above the x-axis.

Explanation:

#y=|3 x + 6 |# is the combined equation for the pair of lines #y=+-(3 x + 6 )#, subject to the condition #y >= 0#.

These two lines cut at #(-2, 0)#

The V-like part of the pair of lines from and above the point of intersection #(-2, 0)# makes the graph.