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Graph the function: Y=x^2+4x+3..

Vertex:

Axis of Symmetry:

Domain:

Range:

 

ANY HELP IS MUCH APRECIATED!! (;

Hayley1  Dec 14, 2015

Best Answer 

 #11
avatar+91039 
+5

Graph the function: Y=x^2+4x+3..

Vertex:

Axis of Symmetry:

Domain:

Range:

 

\(y=x^2+4x+3\)

 

This is a parabola because it is a polynomial of degree 2  (The highest power of x is 2)

 

There is an invisable +1 in front of the x^2    (1 is the leading coefficient)

Since the leading coefficient is positive the parabola is concave up.

 

\(y=x^2+4x+3\\ y=(x+3)(x+1)\\ \)

The roots of the parabola are where y=0

y will equal zero when  x+3=0  and when  x+1=0

roots are x = -3  and x = -1

 

The axis of symmetry will be half way between the roots

x=(-3+-1)/2 = -4/2 = -2

Axis of symmetry is   x = -2

 

When x=-2    y=2^2-4*2+3 = 4 -8 +3 = -1   So the vertex is (-2, -1)

 

 Domain:  \(x \in Z\)  (x can be anything)

 

Range:      \(y\ge-1\)

 

The vertex is where y=-1 so this is the lowest value that y can take.

 

and here is the graph

https://www.desmos.com/calculator/jypgvfhfex

 

Hopefully you can get a lot from this Hayley but if you have questions, make sure you ask :D

Melody  Dec 14, 2015
Sort: 

57+0 Answers

 #1
avatar
0

I guess your question is so difficult no one wants to answer it?

Guest Dec 14, 2015
 #2
avatar+8621 
0

I guess :(

But Melody is an amazing person and is trying to help me!!

( I hope..)

Hayley1  Dec 14, 2015
 #3
avatar
+2

Melody is awesome! I'll pray she helps ya lol.๐Ÿ˜œ

Guest Dec 14, 2015
 #4
avatar+8621 
0

Thanks! 

The struggle is real right now!

Hayley1  Dec 14, 2015
 #5
avatar
0

Huh. Make a post saying that you are losin faith in Melody. That would be funny๐Ÿ˜€

Guest Dec 14, 2015
 #6
avatar+8621 
0

Noo! she would k**l me!!

She wouldn't like me anymore!

crying

Hayley1  Dec 14, 2015
 #7
avatar
0

Hahaha! I can do it for you.

Guest Dec 14, 2015
 #8
avatar+8621 
0

haha. They work there bottoms off to help us!!!!

I greatly appreciate it Melody & Alan.

Thank you a lot!!

Like i said..

Anything is helpful information!

Hayley1  Dec 14, 2015
 #9
avatar+26329 
+5

This should help:

graph

Domain is from -infinity to infinity.  The range is all the valid values of y.  The graph should help you to figure that out.

Alan  Dec 14, 2015
 #10
avatar+8621 
0

Thank you!

But, unfortunaly..

i cannot see it :(

Hayley1  Dec 14, 2015
 #11
avatar+91039 
+5
Best Answer

Graph the function: Y=x^2+4x+3..

Vertex:

Axis of Symmetry:

Domain:

Range:

 

\(y=x^2+4x+3\)

 

This is a parabola because it is a polynomial of degree 2  (The highest power of x is 2)

 

There is an invisable +1 in front of the x^2    (1 is the leading coefficient)

Since the leading coefficient is positive the parabola is concave up.

 

\(y=x^2+4x+3\\ y=(x+3)(x+1)\\ \)

The roots of the parabola are where y=0

y will equal zero when  x+3=0  and when  x+1=0

roots are x = -3  and x = -1

 

The axis of symmetry will be half way between the roots

x=(-3+-1)/2 = -4/2 = -2

Axis of symmetry is   x = -2

 

When x=-2    y=2^2-4*2+3 = 4 -8 +3 = -1   So the vertex is (-2, -1)

 

 Domain:  \(x \in Z\)  (x can be anything)

 

Range:      \(y\ge-1\)

 

The vertex is where y=-1 so this is the lowest value that y can take.

 

and here is the graph

https://www.desmos.com/calculator/jypgvfhfex

 

Hopefully you can get a lot from this Hayley but if you have questions, make sure you ask :D

Melody  Dec 14, 2015
 #12
avatar+8621 
0

Thank you so much!!

You're so so helpful!! 

<3333333

Thaank you, Alan!!

You're very helpful, too!

<3333

Hayley1  Dec 14, 2015
 #13
avatar
0

Not my question but I was getting tired waiting for the answer to that one.

Guest Dec 14, 2015
 #14
avatar+91039 
0

Thank you Hayley and guest for your glowing refernces BUT how am i going to fit my head through any door now????

 

Hi Alan :))

Melody  Dec 14, 2015
 #15
avatar+8621 
0

whatttt...?

:D

Hayley1  Dec 14, 2015
 #16
avatar
0

I just needed to add my 2 cents. Although it ain't worth much๐Ÿ˜€

Guest Dec 14, 2015
 #17
avatar
0

I'll be happy to do it any time... 

Guest Dec 14, 2015
 #18
avatar+91039 
0

All the praise has gone to my head and now it is very swollen so I do not know if it will fit through doorways anymore.  ://   sad

Melody  Dec 14, 2015
 #19
avatar
0

Good one๐Ÿ˜œ๐Ÿ‘Œ๐Ÿผ

Guest Dec 14, 2015
 #20
avatar+8621 
0

LOOOL!!

Hayley1  Dec 14, 2015
 #21
avatar
0

Also Haley1 ya kinda ruin good ( puns etc.) when ya ask for an explanation.

Guest Dec 14, 2015
 #22
avatar+91039 
0

Thanks guest,

You are welcome to put your 2 cents in :))

Melody  Dec 14, 2015
 #23
avatar+8621 
0

Leave me alone!

haha :)

Hayley1  Dec 14, 2015
 #24
avatar+91039 
0

NO Hayley didn't ruin it.

She should always ask when she does not understand :)

Melody  Dec 14, 2015
 #25
avatar+8621 
0

Exxactlyy!!!!

Haa!

She's on my side!!

cool

Hayley1  Dec 14, 2015
 #26
avatar
0

It was the purpose of my creation to annoy people... And I pride myself on being good at it. In fact I have only been slugged 4 times. But they got hurt back so my " attackers" and I are even.

Guest Dec 14, 2015
 #27
avatar
0

Yeah I know she didn't ruin it in this case but I hate it when I have a good comment and then someone asks me to repeat it or something... It just doesn't seem as good the second time around.

Guest Dec 14, 2015
 #28
avatar+8621 
0

So.. Someone should pretty please help me on this..

 

I have a huge project i have to do.. :/

It's on drivers ed!

Hayley1  Dec 14, 2015
 #29
avatar+8621 
0

Can i put pictures on here that i screen shot form my laptop??

Hayley1  Dec 14, 2015
 #30
avatar
0

I should make that my motto " Ask in yo will totally understand" it's sounds a little better than ask and yo shall receive. Don't ya think.

Guest Dec 14, 2015
 #31
avatar
0

What is drivers ed

Guest Dec 14, 2015
 #32
avatar
0

I dunno bout pics.

Can Yo?

Guest Dec 14, 2015
 #33
avatar+8621 
0

uggggghhh.. :/

Hayley1  Dec 14, 2015
 #34
avatar
0

I take it ughhhhhh was response to 3ed post what bout second one.

Guest Dec 14, 2015
 #35
avatar+8621 
0

i dont no how to post pictures that i screen shot :/

Hayley1  Dec 14, 2015
 #36
avatar
0

Neither do I bro! 

Guest Dec 14, 2015
 #37
avatar+8621 
0

pftt Broo.

Your a girl, Right?

Hayley1  Dec 14, 2015
 #38
avatar
0

My #31 question is getting bored.

Guest Dec 14, 2015
 #39
avatar+8621 
0

haha, drivers ed is a class where i can learn to drive better, so that i dont drive crazy ^-^

Hayley1  Dec 14, 2015
 #40
avatar
0

Noooooo. Why the h**l would yo accuse me of being a girl.

Guest Dec 14, 2015
 #41
avatar+8621 
0

hehe. Sowwiee!

What's your namee?

Hayley1  Dec 14, 2015
 #42
avatar
0

JJ I am a girl but I am a tomboy.  My name is Victoria but don't use my name cause I hate it.

Guest Dec 14, 2015
 #43
avatar
0

I've talked to yo before and told yo ma name... I think or that could have been Katie Leigh I told ma name to. 

Guest Dec 14, 2015
 #47
avatar
0

Sup? No one answering ma posts dude that's mean.

Guest Dec 14, 2015
 #48
avatar+8621 
0

im here!

Working on some projectss

Hayley1  Dec 14, 2015
 #49
avatar
0

Cool way projects? Once I made a guillotine but I made it smash a watermelon it was messy but awesome.

Guest Dec 14, 2015
 #50
avatar+8621 
0

LOL! driving project, science project.. Finals study guides

Hayley1  Dec 14, 2015
 #51
avatar
0

Oh... Less awesome. Is yo profile pic of yo I wish I had blonde hair but it would be kinda useless cuz I died ma hair orange and black.

Guest Dec 14, 2015
 #53
avatar+8621 
0

hehehehe

Hayley1  Dec 14, 2015
 #55
avatar+91039 
0

Driver's Ed would stand for Driver's Education.

Hayley can tell you more about what it is :/

Melody  Dec 14, 2015
 #56
avatar+8621 
0

Yupp :)

Its a great class!

Hayley1  Dec 14, 2015
 #57
avatar
0

I'm gonna be 25 fore I can drive a car. I always press gas to hard and the vehicle like goes on two. It is fun though also I e only driven a golf cart and four wheeler. Once I pressed the gas to hard and ma friend fell off she was out for carnage after that.

Guest Dec 14, 2015
 #58
avatar+8621 
0

is that you victoria?

I cannot tell..

So many guests

Hayley1  Dec 14, 2015
 #59
avatar
0

Yeah it's me but I did tell ya not to call me Victoria.

Guest Dec 14, 2015
 #60
avatar+8621 
0

oh, sorry

Hayley1  Dec 14, 2015
 #61
avatar
0

Sok, I gotta go now am mom is probabaly gonna be waking up soon. Peeps who go to school dunno how easy they got it.

Guest Dec 14, 2015
 #62
avatar+8621 
0

LOOL.

Goodbye. (:

Hayley1  Dec 14, 2015

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