graph y=IxI-4....

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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graph y=IxI-4....

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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as evidenced by the co-ordinates of (-4,0) (0,-4) (4,0)? how to get those points mathematically? y=x-4, y=x+4? Or - what did you apply to get those co-ordinates?
Mathematica generated the plot with the following Plot function call: Plot[Abs[x] - 4, {x, -5, 5}, AspectRatio -> Automatic] The absolute value of a signed number is the number with the sign of it stripped off. For positive numbers there is no change. The absolute value of -4 is 4. |-4| - 4 is 4 - 4 = 0. This is the point on the negative x axis. Remember that there is a formula to calculate y given a value of |x|. That is, y = |x|-4. At x = -4 the line crosses the negative x axis because the associated y value is |-4| -4 = 4 -4 which is 0.. When x is 0 the (|0| - 4) = -4. Both lines meet at the point (0,-4) If you did not have to contend with the absolute operator, then the line would be straight and would not change direction at (0,-4).

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One thing I forget to stress is that in evaluating a math expression with absolute values it is probably a good idea to evaluate the absolute values first changing any negative signs inside the two vertical bars to plus, at least in your mind.
Brilliant! This explains it better, I appreciate your thorough response
Thank you and sorry for the delay. I am 76 years old and I am not able to knock out the narrative as fast as a much younger person. Have a good day.
: ) You did great! It's 3:20am here, so I'm reading slow anyway ; )

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