Question

A parabola has the exact same points on ________ sides.

Answer 1

(((
well, assuming the parabola is an explicit function (in alg. when they ask you if something is a function or not, they are referring to this - to whether or not your function is an explicitly defined (explcit) function).
For your parabola to be an explicit function it has to open down or up (not right or left).
)))

So at any value y=a that is on the parabola, the x-coordinates will have the same absolute valuei

Answer 2

I don't really know what they want though-:(

Answer 3

THANK YOU! And same I don't even know what to put for this (btw this is a note taking guide question) Do you think it could be "the same sides"?

Answer 4

but would your note then exactly mean?

Answer 5

this is what I would write in my notes, if this is just for your notes, not for h/w.....

Answer 6

yeah it's a note taking guide question that I'm filling out before I actually do the assignment

Answer 7

I just need to fill in the blank for that.

Answer 8

oh, I actually don't know how to shortly write every thing down.

Answer 9

for a parabola that starts at the origin, that opens up/down.

For any (\(\rm x_n,y_n\)) that is not the origin, it has a corresponding point (\(\rm -x_n,y_n\)) to it.
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for a parabola that starts at the origin, that opens left/right.

For any (\(\rm x_n,y_n\)) that is not the origin, it has a corresponding point (\(\rm x_n,-y_n\)) to it.
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Answer 10

don't think a parabola can have 2 exactly same points (or any one function of \({\bf R}^1\), \({\bf R}^2\) or \({\bf R}^3\), (and certainly not a dot - that is \({\bf R}^0\) cause it itself can have 1 point).

(( in polar coordinates you could have different representations of a point that is placed on the same spout. ))

Answer 11

ok, thank you so much!

Answer 12

yes, sorry that can't fill it in... it seems a little error-ish to me... good luck