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

Question

Kennedy Adams · Accepted Answer

See the 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#

Eva Adamson · Answer

See the Socratic graph and explanation.

#y+10=2|x+6|>=0#. So, #y>=-10#. The equation represents the point of intersection #V(-6, -10) and the V-part of the two lines above #(y-2x-2)(y+2x+22)=0# Proof using algebra: 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# It inserts the Socratic graph. diagram{2|x+6|-10 [-20, 20, -11, 9]}

Hazel Anglin · Answer

undefined To graph the equation $ y = 2| x + 6 | - 10 $, you first need to understand the shape of the absolute value function. The absolute value function $ |x| $ has a "V" shape with its vertex at the origin. When you add or subtract values inside the absolute value function, it shifts the graph horizontally.

For the equation $ y = 2| x + 6 | - 10 $, the graph will shift the graph of $ y = 2| x | $ horizontally 6 units to the left and vertically 10 units down.

So, the vertex of the graph will be at the point $(-6, -10)$, and the shape will be a "V" opening upwards.

You can then plot additional points to sketch the graph, or use the knowledge that the graph is symmetric to complete the sketch.