Question

Determine whether each curve for y=4x^2 is symmetric with respect to the x-axis, the y-axis and the origin.

Answer 1

So, what have you tried so far?

Answer 2

It's actually making alot of sense. So far, all my answers are correct in the back of the book, so now I want to make sure i'm getting the others right. I didn't understand the entire concept until now so its coming together quite well thanks to you. I'm going to submit in here what I have so far, so maybe you could tell me if it looks right if you would be so kind.

Answer 3

y=4x^2

To solve for the x-axis, I have
-y=4x^2
I cannot do anything else with this equation and since it is not the original equation, I am saying there is no x-axis symmetry.

Answer 4

To solve for y-axis, I have
y=(-4x) (-4x)
y=4x^2
Original Equation makes it y-axis symmetric

Answer 5

To solve the origin (replacing with-x, y), I have
y=(-4x) (-4x)
y=4x^2
Origin YES........

I sure hope i'm doing this a bit better...what do you think?

Answer 6

yes you right

Answer 7

Really? That is awesome. I sure have been studying hard considering this isn't even my work. I passed Algebra in 2002 in college with a 100%; however apparently after all those years you forget alot. Its pretty neat though.

Answer 8

yes its true but when you learned something and forget
through some time you remember this very fast

Answer 9

Im not so sure that I got the origin right though. Aren't I replacing x,y with (-x,-y)

Answer 10

no let's see
for example
y=x^3
x-axis is -y=x^3
y-axis is y=(-x)^3

Answer 11

So original equation is y=4x^2

For the origin, shouldn't I be replacing the x,y with (-x, -y)?

Making it:

-y=(-4x) (-4x)
-y=4x^2

Making the origin not symmetric right?

Answer 12

what don't you understand

Answer 13

y-axis for y=4x^2 is origin function

Answer 14

Okay, so correct the first time. Ugh.

Answer 15

I put that on my calculator as well and got what you got as well. Thank you very much again.

Answer 16

Okay, so correct the first time. Ugh.