Question

I need help with 4 questions please and thank you! Also giving medal!!!
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1. Select the point that is on the right side of the vertex of y = |x + 3| + 4.
A) (–5, 6)
B) (–4, 5)
C) (–3, 4)
D) (–1, 6)

2. What is the vertex of y = 2|x| – 1 ?
A) (–1, 0)
B) (0, –1)
C) (0, 1)
D) (1, 0)

3. What is the solution set for |x – 2|– 1 > 2?
A) x > 5 or x < –1
B) x < 5 or x > –1
C) x > –5 or x < 1
D) x < 5 or x > –5

Answer 1

4. Select the inequality of the graph shown below.

A) y greater than or equal to |x + 2| + 1
B) y less than or equal to |x + 2| + 1
C) y greater than or equal to |x – 2| + 1
D) y less than or equal to |x – 2| + 1

Answer 2

@satellite73

Answer 3

hi

Answer 4

how bout we do this one
y = |x + 3| + 4 first

Answer 5

Okay. Thanks.

Answer 6

for the first coordinate of the vertex, set \(x+3=0\) and solve in one step
what do you get?

Answer 7

x = -3

Answer 8

ok good, and the second coordinate of the vertex is that \(+4\) hanging out at the end

Answer 9

so the vertex is \((-3,4)\)

Answer 10

Oh Okay. That is it? Wow, thanks.

Answer 11

this one
What is the vertex of y = 2|x| – 1
is similar only easier, since if you set \(x=0\) there are no steps in solving, first coordinate of the vertex is \(0\) and the second coordinate is that \(-1\) hanging out at the end
so it is \((0,-1)\) and yes, it is that easy

Answer 12

Wow, thanks.

Answer 13

this one
|x – 2|– 1 > 2 start by adding 1 on both sides of the inequality to get
\[|x-2|>3\]

Answer 14

Okay, I am following.

Answer 15

then you have to solve TWO inequalities separately, but both are easy
you get
\[x-2>3\] as one inequality, and \(x-2<-3\) as the other
each is solved in one step
what do you get?

Answer 16

x < - 5 and x > 1???

Answer 17

no, i think your mistake was you subtracted 2 from both sides, but because you have \(x-2\) you want to ADD 2 to both sides to get \(x\) by itself
try again but this time add 2 to both sides

Answer 18

I am confused. :/

Answer 19

Wait.

Answer 20

I got it.

Answer 21

kk

Answer 22

x<1 x>-2?

Answer 23

No, that doesn't seem right. :/

Answer 24

that is because you switched the inequalities by mistake

Answer 25

\(x-2>3\) add 2 to both sides, leave the inequality alone

Answer 26

x > 5

Answer 27

ok good
that is the solution to one of them
now you still have to solve
\[x-2<-3\] and again add 2 to both sides

Answer 28

x < -1

Answer 29

x > 5 and x < -1

Answer 30

got it

Answer 31

YAY

Answer 32

THANKYOU! (:

Answer 33

to be picky and technical it is \(x<-1\) OR \(x>5\) not "and" since no number fits both categories

Answer 34

Okay, thanks.

Answer 35

yw
still one more to go right?

Answer 36

Yep.

Answer 37

#4.

Answer 38

ok so as you can see from the picture, the shaded region is above the two lines, so you know it must be \(y\geq something\)

Answer 39

that means you can ignore answer B and D and only consider A and C

Answer 40

Yes.

Answer 41

It is A.

Answer 42

??

Answer 43

lets go slow here
it takes me a minute to scroll up and see the answers

Answer 44

Okay. Sorry.

Answer 45

A is \(y \geq|x + 2| + 1\) now lets find the vertex of \(y=|x+2|+1\)

Answer 46

first coordinate of the vertex, you set \(x+2=0\) and solve
what do you get ?

Answer 47

did i lose you?

Answer 48

No. I am here.

Answer 49

x = -2

Answer 50

Sorry.

Answer 51

right, so the vertex of\(y=|x+2|+1\) is \((-2,1)\) but that is NOT the vertex in the picture, is it?

Answer 52

No.

Answer 53

you can see from the picture that the vertex, that point on the bottom, is \((2,1)\) and so the graph is of \(y=|x-2|+1\)

Answer 54

So it is C?

Answer 55

that means you are looking at \(y\geq |x-2|+1\)

Answer 56

Okay.

Answer 57

yeah, it is always C

Answer 58

Great thank you so much!!!!

Answer 59

You're a life saver ! (:

Answer 60

yw
you got more or is that it?

Answer 61

That is it for now. (: Thank you so much! I really appreciate it.

Answer 62

no problem hope it was more or less clear in case you have to take a test or something