Question

What is the graph of the absolute value inequality?

Answer 1

\[[x-5] \ge y - 2\]

Answer 2

I like your name, I'll do my best to explain ^^

Answer 3

So let's start with some random plots. What are some sets of values that prove this statement?

Answer 4

x-5 and y-2

Answer 5

I mean ordered pairs, like for example, (8, 2) works.

Answer 6

Oh ok

Answer 7

We can eliminate choices this way, so what graphs already don't work?

Answer 8

In other words, which graphs don't include (8, 2) in their shaded region?

Answer 9

B and D

Answer 10

D I agree with, but why B?

Answer 11

Sorry, C and D

Answer 12

Yep, that's correct. So how about you try and test a point that A has, but B doesn't have? That way we can eliminate one or the other next and get our answer.

Answer 13

I think A is my answer

Answer 14

You are right, but would you care to explain your reasoning? I just want to make sure you got it for the right reasons.

Answer 15

-2 works with A

Answer 16

sans -

Answer 17

Wait a second, I just double-checked this on wolfram, and the graphs don't even match.

Answer 18

Is the inequality written correctly?

Answer 19

Yes

Answer 20

That's weird, because there is actually a different way of doing this. What you can do is rearrange the inequality to look like:

y<= Ix-5I - 2

Answer 21

Sorry, I mean +2

Answer 22

A shortcut to finding the vertex would be to shift the vertex according to the constants inside and outside the absolute value.

Answer 23

So the constant inside the absolute value is -5, and the constant outside is 2. The inside constant means we shift the vertex from the origin 5 units to the RIGHT (if it were +5, left), and the outside constant means we then shift it up 2 units (-2 would have meant 2 units down).