Question 255969
How do the graphs of f(x)= x^2 + x and g(x)= x^2 + |x| compare?
<pre><font size = 4 color = "indigo"><b>
Here's the graph of {{{"f(x)"=x^2+x}}} in red.

{{{ graph(400,400,-5,5,-2,8,x^2+x) }}}

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

Now here's the graph of {{{"f(x)"=x^2+abs(x)}}} in green:

{{{ graph(400,400,-5,5,-2,8,-3, x^2+abs(x) ) }}}

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:

{{{ graph(400,400,-5,5,-2,8,(x-.04)^2+(x-.04), x^2+abs(x) ) }}}

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</pre>