SOLUTION: How do the graphs of f(x)= x^2 + x and g(x)= x^2 + |x| compare?

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Question 255969: How do the graphs of f(x)= x^2 + x and g(x)= x^2 + |x| compare?
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
How do the graphs of f(x)= x^2 + x and g(x)= x^2 + |x| compare?

Here's the graph of %22f%28x%29%22=x%5E2%2Bx in red.

+graph%28400%2C400%2C-5%2C5%2C-2%2C8%2Cx%5E2%2Bx%29+

Notice that it is NOT symmetrical with respect to the y-axis.

Now here's the graph of %22f%28x%29%22=x%5E2%2Babs%28x%29 in green:

+graph%28400%2C400%2C-5%2C5%2C-2%2C8%2C-3%2C+x%5E2%2Babs%28x%29+%29+

Notice that it IS symmetrical with respect to the y-axis,
and has a sharp point at the bottom.

Notice how they look if we put them on the same set of 
coordinate axes:



They coincide exactly on the right of the origin where x is positive,
but on the left of the origin where x is negative the second (green)
graph is the red graph shifted one unit right.

Edwin