Question

Pre-cal 12 Question!
Graphing polynomial equations!

Please do not send me graphing pictures, I know how to use a graphing calculator.

I want to graph it algebraically, Please explain. Thank you

Answer 1

\[x^4 - 4x^3+ 2x^2+ x +4\]

Answer 2

I know it is possible to use synthetic division or long division to find the quotient of this polynomial and using the quotient to find the zeros or solutions of this polynomial.

Is there any other way?

Answer 3

@matt101 do you know about this?

Answer 4

That's the method I would use too, but you need more information to graph the function, such as intervals of increase and decrease (and local max/min values). Figure those out and you'll have a way to fully graph the function!

Answer 5

If it those information are not given. There is no way to find it right? I mean at grade 12 level

Answer 6

No you still can. Is this a question from your calculus class or your functions class?

Answer 7

pre-cal class :D

Answer 8

If it's pre-cal then you're still expected to do this algebraically, but you'll eventually learn that with calculus graphing these guys becomes super easy.

For now you just need to determine the various intervals of the function. The midpoint x-value of those intervals will be the local max/min (plug in a solve for y). Then you can connect the max/min points with the zeros and you'll have your function graphed.

Answer 9

@matt101 ok that makes sense. My teacher has not taught me how to graph these yet using max and min point. I guess I have to stick to synthetic division. :)

Answer 10

Thank you

Answer 11

No problem. There may be a different way other than what I've mentioned, but I'm just used to calculus now because it's much more efficient and don't remember pure algebraic methods as much anymore :P