# How do you sketch the general shape of f(x)=x^4-2x^2+x-2 using end behavior?

One way is to use synthetic division to write the function in the form of $a {x}^{2} + b x + c$.
So here, we have an equation to the 4th degree (${x}^{4} - 2 {x}^{2} + x - 2$). So 4 is even and because we know how a parabola (${x}^{2}$) has two arrows going upward, this graph is also going to do the same thing. graph{x^4-2x^2+x-2 [-10, 10, -5, 5]}