Question

Which inequality matches the graph below?
y > |x + 2| + 1
y < |x - 2| + 1
y > |x + 2| - 1
y < |x - 2| - 1

Answer 1

@mathmate @ganeshie8 can you help me?

Answer 2

You answer is correct, can you explain?

Answer 3

Well I plugged in values :)

Answer 4

It's easier than that!

Answer 5

Lol really?

Answer 6

Do you know that the V-shaped graph is typical of the abs function.?

Answer 7

no

Answer 8

The graph of the absolute value function is typically a V-shape because it's like a straight line passing through the origin, but with the negative part reflected about the x-axis.
Make sense?

Answer 9

ohhh so you would graph it like y=mx+b? then reflect

Answer 10

Yep.

Answer 11

All this is to say that
y=|x| has a vertex at (0,0)

Answer 12

so far so good?

Answer 13

yes ;)

Answer 14

Now look at your graph, where has the vertex gone?

Answer 15

the same place? (0,0)

Answer 16

I see the vertex at (2,1), do you?

Answer 17

(-2,1)

Answer 18

I mean the graph,the white part!

Answer 19

oh yeah lol

Answer 20

Now, any translation of the vertex to (h,k), the equation of the absolute value function is modified to
y=|x-h|+k
If you substitute h=2, k=1, you will get the answer B, without ANY calculation!

Answer 21

I see now. Just pretty much plug in the vertex and use the formula for the equation

Answer 22

Exactly!
A bonus, if you have time!

Answer 23

:)) yayyyy I understand! Thank you so much! :)

Answer 24

sure,love to learn

Answer 25

The same idea applies to parabolas (in fact, any other curves) as well.
A parabola with vertex at (0,0) is y=x^2.
So a parabola with vertex at (5,3) would be
y=(x-5)^2+3
Makes sense?

Answer 26

yes! :) so knowing the formulas are important for each graph to find the equation

Answer 27

Yep! Hope that makes your other problems easier to solve!

Answer 28

yep :) thx again!

Answer 29

You're welcome! :)