How do you graph y=xabs(2x+5)?

1 Answer
Jan 19, 2018

Read below.

Explanation:

Let's think of it this way:
abs (a)=a and abs (-a)=a

For our first case, we are just bringing out a outside the absolute value.
For the second case, we are finding the opposite of whatever was inside the absolute value sign.

So we can say that:
When 2x+5>=0, then abs (2x+5) =2x+5
When 2x+5<0, then abs (2x+5)=-2x-5

Let's apply this to our function.
When 2x+5>=0, then y=x(2x+5)=>y=2x^2+5x
When 2x+5<0, then y=x(-2x-5)=>y=-2x^2-5x
We first garph these two parabolas:
desmos.comdesmos.com
Now, we ask ourselves,"For what values of x does 2x+5>=0hold true?"
Similarly, "For what values of x does 2x+5<0 hold true?"

To find out the answer, we solve each inequality.
2x+5>=0
2x>=-5
x>=-5/2

2x+5<0
2x<-5
x<-5/2

This is actually telling us that for any x values greater than or equal to -5/2, the blue parabola will apply. When x is smaller than -5/2, then the red parabola will apply. The green graph is the graph of our function.
So we now have:
Desmos.comDesmos.com

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