Question

Draw the graph of the polynomial $f\left(x\right)=x^2-6x+9$.

Answer 1

SOLUTION Let y = f(x) or, $y=x^2-6x+9$.
The following table gives the values of y or f (x) for various values of x.

x	-2	-1	0	1	2	3	4	5	6	7	8
$y=x^2-6x+9$	25	16	9	4	1	0	1	4	9	16	25

Thus, the graph of $y=x^2-6x+9$ passes through the points (-2,25), (-1,16), (0,9), (1,4), (2,1),(3,0),(4,1),(5,4),(6,9),(7,16)and (8,25).Let us plot these points on the graph and draw a free hand smooth curve passing through these points. We observe that the vertex of the parabola is at point P (3,0) as shown in Figure.