# Write an Absolute Value System of Equations

I am confused just trying to draw the diagram for this problem, much less how to apply the Algebra. Moreover, it wants a system of absolute value equations. Is that because the balls will go up and down?

[OK - per request and downvote, I have attempted to draw this diagram several times and am unable to get farther than a basic idea of the person relative to the ceiling. I lose my perspective when they talk about the tile borders. I am not at all sure what that means or how to gauge that in the calculations.

Furthermore, as I said originally, I am not able to understand why this is an absolute value problem to begin with. This problem did not come with an associated textbook, and the student who is requesting assistance has no references whatsoever. I am not only doing the work and making sure he gets what he needs, but also attempting to provide him references for later when he needs refreshing/reminders. I don't understand how he is being taught...

So, anyway, I will not die without assistance, but I have put a lot of time into this (with a Math degree and quite exhaustive IT skills and research). I don't understand what they are asking or why they are asking it, quite honestly, and I am not sure if I can say it any better than that, LOL.]

Any help is greatly appreciated.Absolute Value System of Equations

• I think you could've added the question in to paragraph, and what gets you confused? Perhaps if you can open it up a little bit, we could be more helpful. – Deniz Tuna Yalçın Sep 24 '17 at 14:34
• It looks like the question was cut off. Are the coordinates for Joe's launch point $(0, 6)$? – N. F. Taussig Sep 24 '17 at 20:22

We know that each tile is $2$ feet wide. Since Joe releases his ball from directly beneath a tile border and it hits the middle of the tile that is two tiles from the border under which he is standing, the ball hits the ceiling $$2~\text{ft} + \frac{1}{2} \cdot 2~\text{ft} = 3~\text{ft}$$ away from him horizontally. Since he releases the ball six feet above the ground and the ceiling is eight feet high, the ball hits the ceiling at the point $(3, 8)$ if we assume he releases it at the point $(0, 6)$.

Since Zoe releases her ball toward Joe from the point $(12, 6)$ and the ball hits the ceiling at the border three tiles away from her head, the ball hits the ceiling six feet away from her horizontally. Therefore, it hits the ceiling at the point $(6, 8)$.

Why is this an absolute value problem?

The balls reflect off the ceiling.

Therefore, the vertical position of Joe's ball can be modeled by an absolute value graph with vertex $(3, 8)$ that passes through the point $(0, 6)$. To find the height at which Zoe will catch the ball, we need to know how high the ball will be when $x = 12$.

The vertical position of Zoe's ball can be modeled by an absolute value graph with vertex $(6, 6)$ that passes through the point $(12, 6)$. To find the height at which Joe will catch the ball, we need to know how high the ball will be when $x = 0$.

Can you take it from here?

• I think so. Thank you SO much!! I really appreciate your time and help. – J.E.M. Texas Sep 24 '17 at 20:55