Question

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

Answer 1

what is it?

Answer 2

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.

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

which means ?

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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 :)

Answer 13

i just graphed it on Desmos lol

Answer 14

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

Answer 15

...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

Answer 16

okok thank you

Answer 17

And no I never get annoyed...

okay thats a lie..but you're good XD

Answer 18

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

Answer 19

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

Answer 20

still alive ?

Answer 21

if so this is my next question

Answer 22

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.

Answer 23

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

Answer 24

btw #4 is the question u just helped muah with

Answer 25

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 :)

Answer 26

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

Answer 27

-16 *****

Answer 28

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)

Answer 29

okay okay

Answer 30

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

Answer 31

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)



We know the slope between (0,-16) and (4,0) is 4 right? what is the slope between these 2 new points?