Hello, Punch!
The equation of a curve is .
It shows that the curve has a minimum point of (4,1).
Now, if I have a modulus of this equation, that is: ,
. . the turning point would be (4,1).
Is the turning point a maximum point or minimum point now? Visualize their graphs . . .
The graph of the parabola looks like this: Code:

 * *


 * *

+**
 * *
 * *
 *

There is an absolute minimum at (4, 1).
There is no maximum.
With absolute values, any point below the axis
. . is reflected upward.
The graph of the modulus function is:
Code:

 * *

 *
 * * * *
 * *
+**
 3 5

It has absolute minimums at (3,0) and (5,0).
. . and a relative (local) maximum at (4,1).