Question

Draw the graph ofthe polynomial $f\left(x\right)=-3x^2+2x-1$.

Answer 1

Let y = f(x) or, $y=2x^2-4x+5$.
The following table gives the values of y for various values of x:

x	-3	-2	-1	0	1	2	3	4	5
$y=2x^2-4x+5$	35	21	11	5	3	5	11	21	35

Thus, the graph of y = 2x2 - 4x + 5 passes through the following points:(-3,35), (-2,21), (-1,11), (0,5),(1,3), (2,5),(3,11),(4,21), (5,35) etc. '
Let us plot these points on a graph paper and draw a smooth free hand curve passing through these points to obtain the graph of $y=2x^2-4x+5$as shown in Figure