Question

Draw the graph of y = (x – 1) (x + 3) and hence solve x² – x – 6 = 0

Answer 1

y = (x – 1) (x + 3)

y = x² + 2x – 3

(i) Draw the graph of y = x² + 2x – 3 by preparing the table of values given below

x	– 4	– 3	– 2	– 1	0	1	2	3	4
x2	16	9	4	1	0	1	4	9	16
2x	– 8	– 6	– 4	– 2	0	2	4	6	8
– 3	– 3	– 3	– 3	– 3	– 3	– 3	– 3	– 3	– 3
y	5	0	– 3	– 4	– 3	0	5	12	21

(ii) Plot the points (– 4, 5), (– 3, 0), (– 2, – 3), (– 1, – 4), (0, – 3), (1, 0), (2, 5), (3, 12) and (4, 21) on the graph sheet using suitable scale.

(iii) To solve x² – x – 6 = 0 subtract x² – x – 6 = 0 from y = x² + 2x – 3

(iv) Draw the graph of y = 3x + 3 by preparing the table.

x	– 4	– 2	0	2	3	4
y	– 9	– 3	3	9	12	15

(v) The straight line cuts the curve at (– 2, – 3) and (3, 12).

Draw perpendicular lines from the point to X-axis.

The line cut the X-axis at – 2 and 3.

The solution set is (– 2, 3)