Question

So I need to understand how to solve this type of problem...

y=(x+2)^2-6
y-2+x

I think by...substitution? And I know you probably have to foil at some point but I have tried this problem so many times and I can't figure it out.

Answer 1

do you mean y=2+x for the second function?

Answer 2

And what are you trying to solve for?

Answer 3

my bad I meant y-2=x

silly shift key :)

the directions only said solve...I am assuming it meant solve the system of equations

Answer 4

So we have \(y=(x+2)^2-6 \\ y-2=x\)

Answer 5

is that what yu have?

Answer 6

I'm gonna let Mr. Mathlete take it from here

Answer 7

Yes

Answer 8

let us substitute x for y-2 in equation #1

Answer 9

so to get \(y=(y-2+2)^2-6\)

Answer 10

you can see that i replaced x by y-2 right?

Answer 11

Yeah

Answer 12

ok now just simplify that more
\(y=y^2-6\)

Answer 13

-2 +2 cancel out

Answer 14

now it need more clean up
\(y^2-y-6=0\)

Answer 15

i subtract y from both sides to get that

Answer 16

what kind of equation is that?

Answer 17

Okay I see what you're doing, i'm not sure what you mean though, by what kind of equation?

Answer 18

i meant that's a quadratic equation, you should have faced it various times?

Answer 19

Yes, but honestly I didn't recognize that; in my math class we don't really do much with the vocabulary for things, unfortunately.

Answer 20

vocabulary is really part of mathematics

Answer 21

we need a language to cross our ideas!

Answer 22

Haha very true.
So, is there anything more that needs to be done to the problem? Or, is that the type of answer they are looking for?

Answer 23

so back to our mean thing.
\(y^2-y-6=0 \Longrightarrow (y-3)(y+2)=0 \)

Answer 24

that is called factoring
and we are not done until we figure out what x is and y

Answer 25

now we pretty much close in finding y

Answer 26

ooooh

Answer 27

any idea what to do with \((y-3)(y+2)=0\)

Answer 28

Um to solve for y you set them both equal to zero?

Answer 29

yes

Answer 30

okay so y=3 and y=-2 right?

Answer 31

yep!

Answer 32

so we got two values for y
we take one value at a time and look for x

Answer 33

to find x we go back the equations we started with

Answer 34

what equation do you think is easier to spit out an answer for us

Answer 35

the second one

Answer 36

yes

Answer 37

now pick one y value you found and plug it to that equation and find x

Answer 38

so x=1 and -4?

Answer 39

oh you already tried both values of y

Answer 40

yes that good answers
(1, 3) and (-4, -2)

Answer 41

the answer is two points

Answer 42

Okay.
Thank you so much, I understood this a while ago, but I completely forgot. You jogged my memory!!

Answer 43

geometrically this mean line y-2=x intersects the parabola y=(x+2)^2-6
in two points

Answer 44

no problem :)

Answer 45

let me show you what is happening Geometrically

Answer 46

http://prntscr.com/9ptxlx

Answer 47

Okay
I see :)
Thanks again!

Answer 48

it's also important to see other interpretations