Question

Draw the graph of the cubic-polynomial $f\left(x\right)=x^3-2x^2$.

Answer 1

Let y = f(x) or, $y=x^3-2x^2$.
The following table gives values of y for various values of x:

$x$	-3	- 2	-1	0	1	2	3	4
$y=x^3-2x^2$	-45	-16	-3	0	-1	0	9	32

Thus, the curve $y=x^3-2x^2$ passes through the points (-3, -45), (-2, -16), (-1,-3), (0,0), (1, -1), (2,0), (3,9), (4,32) etc. Plotting these points on a graph paper and drawing a free hand smooth curve passing through these points, we obtain the graph of the polynomial as shown in Figure.