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

Vertex:

Axis of Symmetry:

Domain:

Range:

__ANY HELP IS MUCH APRECIATED!! (;__

Hayley1
Dec 14, 2015

#11**+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

#2**0 **

I guess :(

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

( I hope..)

Hayley1
Dec 14, 2015

#5**0 **

Huh. Make a post saying that you are losin faith in Melody. That would be funny๐

Guest Dec 14, 2015

#8**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**+5 **

This should help:

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

#11**+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**0 **

Thank you so much!!

You're so so helpful!!

<3333333

Thaank you, Alan!!

You're very helpful, too!

<3333

Hayley1
Dec 14, 2015

#14**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

#18**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. ://

Melody
Dec 14, 2015

#24**0 **

NO Hayley didn't ruin it.

She should always ask when she does not understand :)

Melody
Dec 14, 2015

#26**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**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**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

#30**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

#39**0 **

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

Hayley1
Dec 14, 2015

#42**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**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

#49**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

#51**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

#55**0 **

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

Hayley can tell you more about what it is :/

Melody
Dec 14, 2015

#57**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