# Thread: Help with graphing polynomials

1. ## Help with graphing polynomials

Hi, new here.

I was wondering how can you get a fourth degree polynomial with a graph that only has 1 turn?

This is the problem: 5x^4 +15x^2 + 10

I thought the number of turns (or "bumps" as my teacher calls them) could be determined by "n-1"; n being the exponent of the leading coefficient. So, I thought this questions should have 3 turns, because 4-1= 3.

(Hope I used the correct names for things here. I usually get confused with math terminology.)

Welcome aboard!

Can you get a 4th degree polynomial with a graph that only has 1 turn?

This is the problem: . $y \:=\:5x^4 +15x^2 + 10$

I thought the number of turns is determined by $n-1$,
. . $n$ being the exponent of the leading term. , This is true (sort of).

So, I thought this graph should have 3 turns.

A quartic function, $y \:=\:ax^4 + bx^3 + cx^2 + dx + e,$ can have three turns.

. . and is shaped like: . $\backslash / \backslash / \;\;\text{ or }\;\;/ \backslash / \backslash \$

But if some of terms are missing, some of the bumps may "smooth out".

The extreme case is: $y \:=\:x^4$, which resembles a parabola.