can someone pls help me with some questions involving algebra 2 ? PPPPPPPPPPPPPPPLLLLLLLLLLLLLLLLLEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAASSSSSSSSSSSSSSSSSSSSSSEEEEEEEEEEEEEEEEEEEE

- rebeccaxhawaii

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- jamiebookeater

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- timbo5lice

what is it?

- rebeccaxhawaii

okay so my equation is x^2-16 and it says to Identify the key features of your graph. and
Explain how to find them algebraically.

- johnweldon1993

Well, it would be an upwards facing parabola with a vertex *minimum point* at y = -16

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## More answers

- johnweldon1993

I only know that because the equation of a parabola *or quadratic* is \(\large ax^2 + bx + c\)
So now the key features you can find from this are the minimum point and the point(s) where the parabola crosses the 'x' axis

- rebeccaxhawaii

so yes i understand that part of the vertex on -16 and facing upward but i dont understand like what they are asking for

- johnweldon1993

Well basically they want to know how you can solve for those algebraically

- rebeccaxhawaii

which means ?

- johnweldon1993

So remember how I said the equation of a parabola is \(\large y = ax^2 + bx + c\)
How do you find the vertex if you cannot see the graph? well you use the equation \[\large -\frac{b}{2a}\]
And then how would you find where the parabola crosses the x-axis? You could factor it, or use the quadratic formula

- rebeccaxhawaii

im sorry i am so lost dont i just tell them how i got my answer ?
idk

- johnweldon1993

Yeah that's it, dont overthink it :)
They want to hear, okay what do you think the vertex is based on the graph? Then back that up by actually solving for it
and they want to know when the graph crosses the 'x' axis...and then tell them how you would solve for that

- rebeccaxhawaii

it passes x at -4 and 4 right ? and i say i got -16 vertex because f(x)=x^2-16 the last number is the vertex

- johnweldon1993

The -4 and 4 are correct yes *and you solved that using what method?*
And well the vertex is at the point (0,-16) *I remember losing points because of that one time >.< lol but yeah other than that you're good :)
*****also, the last number is not ALWAYS the vertex :)

- rebeccaxhawaii

i just graphed it on Desmos lol

- rebeccaxhawaii

but ik im probably annoying you with stupid question but could you spare a little more time

- johnweldon1993

...I dont think they'll take that as an answer ;) XD
But no, say you used the quadratic formula to solve for that -4 and 4

- rebeccaxhawaii

okok thank you

- johnweldon1993

And no I never get annoyed...
okay thats a lie..but you're good XD

- rebeccaxhawaii

hold on let me write my answers down but i have another question so prepare yourself for frustration

- johnweldon1993

....I might need a snack for this... XDD I'll be ready!!

- rebeccaxhawaii

still alive ?

- rebeccaxhawaii

if so this is my next question

- rebeccaxhawaii

Using your graph from question 4, describe if the average rate of change is increasing or decreasing, from left to right. Justify your observations by comparing the slopes calculated between at least three different pairs of points.

- johnweldon1993

...barely... haha yeah I'm here :P

- rebeccaxhawaii

btw #4 is the question u just helped muah with

- johnweldon1993

I mean we can really just LOOK at it and see...but I guess we need 3 points on the parabola for justification...tell me 3 points :)

- rebeccaxhawaii

(-4,0) (4,0) (0,16)

- rebeccaxhawaii

-16 *****

- johnweldon1993

Haha cheater :P I wanted different ones...but oh well I didnt specify lol
Oh so calculate the slopes between (-4,0) and (0,-16) and then the slope between (0,-16) and (4,0)

- rebeccaxhawaii

okay okay

- rebeccaxhawaii

u probably know this by just looking at it but us less fortunate beings have to write it down lol so the slopes are -4 and 4

- johnweldon1993

XD I knew it from looking at the 2 points actually XD you get good at this after a while lol
and hmm...i dont wanna confuse you...you are correct, but these points wont work
Lets choose 2 other points like...(4,0) and (5,9)
|dw:1446498829900:dw|
We know the slope between (0,-16) and (4,0) is 4 right? what is the slope between these 2 new points?

- rebeccaxhawaii

still 4

- rebeccaxhawaii

I DID IT WITHOUT PAPER IM MOVING UP IN THE WORLD

- johnweldon1993

....hmm....you sure?

- johnweldon1993

Lol you are moving up in the world...but double check it to make sure XDD

- rebeccaxhawaii

damn this is embarrassing

- rebeccaxhawaii

i was way off okay my new and improved answer is 9

- johnweldon1993

...what is...i have no idea what you're talking about...you never said that... ;P

- johnweldon1993

Oh good your 1 and only answer is 9...awesome you're correct :D lol

- rebeccaxhawaii

YAYYYY

- johnweldon1993

haha okay so since going from left to right...we went from a slope of 4...to 9....what can we say?

- rebeccaxhawaii

that the rate of change is 5 i have no clue

- johnweldon1993

Lol no remember the question
Using your graph from question 4,
*****************describe if the average rate of change is increasing or decreasing, from left to right.*******************
Justify your observations by comparing the slopes calculated between at least three different pairs of points.

- rebeccaxhawaii

it is increasing and moving to the right ?

- johnweldon1993

Well it's not moving anywhere...the graph wont move
But as we evaluate the function going from left to right...the average rate of change is increasing

- rebeccaxhawaii

yes so its increasing but thats it ?

- johnweldon1993

Yeah, that's literally all the question asks for...they want to know if its increasing going from left to right...thats it
Then justify it by using the slope between points like we did

- rebeccaxhawaii

now you sir john are a saint thank you for all your help

- johnweldon1993

Lol not a problem :)

- rebeccaxhawaii

sadly youll probably be getting more questions from me

- johnweldon1993

...oh geez
XD lol it's no problem at all...as long as I'm on of course :P

- rebeccaxhawaii

so this will not be the last of our math bonding but where ya from

- rebeccaxhawaii

so i can get the time zones right

- johnweldon1993

Lol no, we shall learn much more of each other through math haha
I'm MA so EST

- rebeccaxhawaii

okay i promise i wont stalk you

- johnweldon1993

...I mean...my windows are locked for the winter so you couldnt if you tried x) lol

- rebeccaxhawaii

oh great window picking is my specialty

- johnweldon1993

ANDDDDDDD going to buy guard dogs XD :P
dont take them too!!!! not allowed!!!

- rebeccaxhawaii

steak

- johnweldon1993

....NOOOOOOOOOO!!!!! haha they'll follow you like rabbits wanting the 1 big carrot!!
damn...stealthy...I'll find your weakness!! >.<

- rebeccaxhawaii

fun fact for you
carrots are actually not very good for rabbits it gives then diarrhea

- johnweldon1993

...:O its the cause of the pellets!!!!???? actually never knew that!

- rebeccaxhawaii

rabbit poop looks like papaya seeds or circular pellets but when they eat carrots or lettuce there poop becomes like diarrhea which gets caught in there fur quite gross

- johnweldon1993

....hmm...I feel this isnt related to math anymore XD haha jk interesting facts!!!

- rebeccaxhawaii

no john we are now life long friends (sorry forgot to tell you) but yes our friendship destroys the laws of friendship which is not limited to math and lifesaving facts

- johnweldon1993

...Well I knew it was coming eventually....alright
Fish or steak at my wedding? XDDDD Dont worry you'll be seated at my table...only for my bestfriend x) lol
*not gettng married dont worry XD

- rebeccaxhawaii

definitely steak but good dont TRAP YOURSELF just yet you have your whole life ahead of you

- rebeccaxhawaii

when i say shot gun you say wedding

- rebeccaxhawaii

shot gun

- johnweldon1993

XDDD damn I dropped the ball on that XDD sorry lol WEDDING!!!!

- rebeccaxhawaii

wedding:
a spiffy ceremony in which two people get married only to divorce/kill eachother a year later.

- johnweldon1993

^ a truer statement has never been said
REALLY gotta get that into the dictionary lol

- rebeccaxhawaii

its ultimately your choice though

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