Question

NEED HELP WITH Investigating Quadratics

Answer 1

it has that answer but with a +2 at the end

Answer 2

Can you post the options please? :)

Answer 3

f(x) = (x + 5)2 + 2
f(x) = (x - 5)2 + 2
f(x) = - (x - 5)2 + 2
f(x) = - (x + 5)2 + 2

Answer 4

wait no its not showing the -1/12 and 1/12

Answer 5

Weird :(

Answer 6

so the first two have positive 1/12's and the last two have -1/12's

Answer 7

It's positive

Answer 8

and x+5, not x-5

Answer 9

but what about the last +2 ?

Answer 10

That's supposed to be there, they just moved it to the right side instead of the left, guess they wanted y/f(x) to be isolated.

Answer 11

oh okay gotcha

Answer 12

Do you understand how I used that same technique as the last question? It's just the distance from the focus to any point on the parabola.

Answer 13

That's how you get the (x-_) and (y-_)s :)

Answer 14

Derive the equation of the parabola with a focus at (-5, -5) and a directrix of y = 7

Answer 15

Same thing. I'll write it out differently and see if you can try to solve it :) \[\sqrt{(x-a)^2+(y-b)^2}=\sqrt{(y-c)^2}\]Plug in -5 for a and b and 7 for c.

Answer 16

Think you can try it out yourself this time?

Answer 17

ill try can you stay here to check my answer ?

Answer 18

Of course!

Answer 19

so x would be a and y would be b ?

Answer 20

Yes

Answer 21

I just wrote it out like that so it would be easier for you to plug in the values :)

Answer 22

okay thank you :)

Answer 23

No problem :)

Answer 24

wait im confused

Answer 25

What part did you get to?

Answer 26

theres an x and a in the equation but i thought they were the same thing

Answer 27

lol I just put a, b and c so it would be easier to plug the values in... so you have (-5, -5) and y=7. I had it where (a, b) = (-5, -5) and c=7

Answer 28

Sorry to confuse you. I'll write it out for you.\[\sqrt{(x-(-5))^2+(y-(-5))^2}=\sqrt{(y-(7))^2}\] This make more sense to you?

Answer 29

oh okok thank you

Answer 30

:) no problem :)

Answer 31

okay so what now i put it in the equation what do i simplify first

Answer 32

You need to get rid of the squareroots first, which you simply just square both sides and it goes away, giving you\[(x+5)^2+(y+5)^2=(y-7)^2\] which you then expand the (y+5)^2 and (y-7)^2. think you can do that?

Answer 33

wouldnt you take the 2's away or exponents to square ?

Answer 34

Nope

Answer 35

okay wait but we got rid of the square root sign ?

Answer 36

Yep

Answer 37

bbut how we cant do that without changing the problem i thought

Answer 38

Nope, there's nothing wrong with doing that

Answer 39

IM SO CONFUSED THATS AGAINST THE LAWS OF MATH

Answer 40

No it's not haha

Answer 41

no ? ookay

Answer 42

@TheSmartOne :)

Answer 43

can you finish explaining ? okay so you take away the square root and it doesnt change the equation

Answer 44

Nope, so now, we have \[(x+5)^2+y^2+10y+25=y^2-14y+49\]right?

Answer 45

oh i get it because you took the radicals from both sides

Answer 46

Yes

Answer 47

okay got it

Answer 48

Then, we subtract the y^2+10y+25 from both sides to get \[(x+5)^2=-24y+24\]

Answer 49

then \[(x+5)^2=-24(y-1)\]\[y-1=-\frac{1}{24}(x+5)^2\]\[y=-\frac{1}{24}(x+5)^2+1\]

Answer 50

omg thank you im doing to note this down and make a new question so i can give you anothr medal

Answer 51

Okay

Answer 52

No problem