How to sketch a cubic polynomial? How do you sketch $-4x^3+15x-1 = 0$? Any help would be appreciated!

As it's cubic, you determine the orientation - that it has $-4$ in front of the $x^3$ tells you that it will be positive for very negative values of $x$ and negative for very positive values of $x$. So it will start in the second quadrant, and end in the fourth quadrant.
Now, determine the $y$ intercept (let $x=0$) and the $x$ intercepts (solve the equation you provided). Then determine the turning points (find the $x$ where the derivative of the function is zero, then the $y$ value at that $x$). Then it's just a matter of plotting those points, joining them with something resembling a cubic.
