Question

How would I find the x and y intercept for f(x)=-1/(0-2)^2?

I know I have to make x=0 for y and y=0 for x, but I'm not sure I know how to solve it.

Answer 1

That zero that's already there is an x right?

Answer 2

Oh yeah my bad, yes it's supposed to be a x. So the equation is f(x)=-1/(x-2)^2. Sorry lol.

Answer 3

Lol no you're fine!
So yep, for y-intercept, you plug in 0 for x.
So y=-1/(0-2)^2
Order of operations say you do what's in parentheses first, then exponents.
So, y=-1/(-2)^2
So y= -1/4
Are you good so far?

Answer 4

Yeah I am. And then next would I bring 4 to the other side by multiplying?

Answer 5

Nope, you've already got y by itself, so -1/4, or (0, -1/4) is the y-intercept :)

Answer 6

Ohhh, yeah that makes sense. Lol I'm so out of it today, I'm wayyyyy to tired.

Answer 7

But to find x is confusing me. Like I know I'd set it up as 0=-1/(x-2)^2. But from there I'm confused.

Answer 8

Oh jeez, that is weird
So (x-2)^2 is the same as (x-2)(x-2)
So you'd FOIL/clam shell/whatever your method is for that first

Answer 9

Should I say it, and use it as an example or do you wanna try first lol

Answer 10

Let me try it first real quick, I needa practice anyways :)

Answer 11

I figured! I'm an answer-blurter, so I stopped myself hahaha

Answer 12

Ok so I got 0=-1/x^2-4x+2

Answer 13

Eep, so close, the last number is 4, since -2 times -2 is 4.
Shizzzz you didn't even need to do that though now that I look at the overall answer. Good practice though, dont kill me ;)
But what they wanted you to do was flip the fraction (with (x-2)^2 from the bottom to the top)
That makes the whole thing positive so it'll look like
0=(x-2)^2 /1
Then square root everything like
\[\sqrt{0}=\sqrt{(x-2)^{2}}\]
Which leaves
0= + or - (x-2)
Moving the two over makes
x= 2 and -2
^So those are you intercepts. Ugh sorry for the confusion at first, I hope this helps!!

Answer 14

Oh right! Lol I must be really tired, I did get 4 at first I just wrote down 2. Ugh, school just started so my brain isn't used to this yet. But ok, that makes sense. I just don't know why you'd flip it.

Answer 15

Well if you left it how it was, like
0=-1/(x-2)^2, the only way to try and solve it would be multiplying both sides by the denominator to cancel it out.
But that would leave 0=-1, which is not true.
So when things like that happen, the answer would be undefined.
BUT in this case, we could flip it, and still come out with x intercepts. Usually undefined as an answer for intercepts doesnt make sense anyway.
Does that make sense or am I just frying your brain more? Lol

Answer 16

Ok yeah that makes sense. I just didn't know you were allowed to flip it and all.

Answer 17

Yep! You can flip fractions, but when you do, the whole top and bottom need to switch. And if it was a positive fraction, it becomes negative. Negative fractions become positive.

Answer 18

It's called reciprocals if you wanna google for later or something

Answer 19

Oh yeah I remember, ok yeah that makes sense. Thanks so much :) btw quick question, are you good at rational functions? With the whole asymptotes and all that? I'm in precal btw.

Answer 20

Ugh pre-cal was my worst math year tbh. I was failing until like the very end when we got extra credit and exempted assignments for random crap lol so I probably wouldn't be the ebst person to ask :/

Answer 21

Oh that's fine, thanks for you help tho. I really appreciate it, I wouldn't have been able to do my hw otherwise.

Answer 22

Haha aw no problem! Good luck!