How do you graph #y=2abs(x+6)-10#?

2 Answers
Feb 12, 2017

Answer:

See the explanation

Explanation:

The bit inside the | | can be positive or negative but writing it like #|x+6|# always turns the answer to that part into being positive. As a graph it becomes:

At #x-6# we have:

#y=2|-6+6|-10" "->" "y=2(0)-10 = -10#

Tony B

Feb 12, 2017

Answer:

See the Socratic graph and explanation.

Explanation:

#y+10=2|x+6|>=0#.

So, #y>=-10#.

The equation represents the point of intersection #V(-6, -10) and the

V-part above, of the pair of lines

#(y-2x-2)(y+2x+22)=0#

Algebraic proof:

In addition to #y >= -10#,

#y+10=2(x+6)#, giving # y-2x-2=0#, when #x >=-6# and

#y+10=-2(x+6)#, giving # y+2x+22=0#, when #x<=-6#

The Socratic graph is inserted.

graph{2|x+6|-10 [-20, 20, -11, 9]}