what is integral coefficient? (1 Viewer)

[totallybord]

hi
i was just wondering if soemone could tell me what integral coefficient is in a polynomial?
thank you

 

[SoulSearcher]

Any coefficient of a polynomial term that is an integer i.e. the negative and positive whole numbers and the number 0. I might be well off though.

 

[totallybord]

hi
umm how wld u graph a polynomial with an exponent of 4 like (x-1)^4 ?
thanks

 

[pLuvia]

Use calculus methods, find turning points, etc

 

[totallybord]

umm i havent learnt calculus yet... can soemone do a graph of what (x-1)^4 woudl look like?
thanx a lot

 

[Riviet]

The curve is shaped like a very steep parabola with vertex (1,0) and y-intercept 1.

 

[totallybord]

so there's nothing specially shaped for a ^4 ? its just a parabola?

 

[airie]

If it's just a single term kx⁴+c (where k and c are constants) then yes, just a parabola, except it's flatter in the interval [-1, 1] and steeper when x<-1 and x>1. But it can also make an M or W shape (depends on the sign of k) when the polynomial is, say, x⁴-x²+4, where there are more than just one x term.

 

[Raginsheep]

Its not a parabola. A parabola is a specific locus which x⁴ does not obey. It is shaped in a similar manner to a parabola though.

 

[totallybord]

i heard that you can write it as ((x-1)^2)^2 so its a parabola squared?? so i still dun get how u draw that ....

 

[Raginsheep]

It may be a parabola squared. But airie said it was a parabola which I pointed out was wrong. Just because x² is x squared, doesn't still make it a linear line.

 

[SoulSearcher]

You can see how the curve is drawn using this:
http://www.e-tutor.com/et2/graphing/
Just type in (x-1)^4 into the box to see what it looks like.

 

[totallybord]

omg thank you soooooo much

 

[airie]

It is shaped in a similar manner to a parabola though.

Yeah, that's what I meant Not very specific diction there

All even powers look like parabolas, (the higher the power, the more it looks like a beaker).

But some would have 'bumps' for x values near its axis of symmetry, making a W or M shape - like the x⁴-x²+4 mentioned above

 

[SoulSearcher]

But some would have 'bumps' for x values near its axis of symmetry, making a W or M shape - like the x⁴-x²+4 mentioned above

And that's where calculus comes into play, to figure out those turning points and such.

 

[totallybord]

ummm is (x^2 -1)... wld u graph it as a parabola?
im a bit confusedd
thanks for ur help :d

 

[pLuvia]

Draw and normal parabola y=x² and shift it 1 unit right

 

[SoulSearcher]

Isn't the normal parabola graph shifted 1 unit down for that graph?

 

[airie]

Isn't the normal parabola graph shifted 1 unit down for that graph?

Yeah I think that's what he meant. (x-1)² would be the standard parabola shifted 1 unit to the right.