Question

y =−6x^4−9x^3+105x^2
Could someone help me and explain what and how to use the leading term test to describe the end behavior?

Answer 1

So we only want to look at the term that has the highest power. The rest of the polynomial doesnt help us determine end behavior. So if the highest power of your polynomial is odd, you have these two possibilities



When I say positive/negative, I just mean the sign of the term. So something like x^5 would follow the end behavior of the left pictures and something like -2x^7 would follow more like the right picture.

If the highest power of your polynomial is even, we get these two possibilities.



So an obvious match for the left picture would be x^2, while something like -x^6 would more match the right picture.

So for you, youre highest power term is -6x^4. Because the power, 4, is even and the term itself is negative, I would have this kind of end behavior:



Kinda make sense?