Question

Draw the graph of y = 2x² – 3x – 5 and hence solve 2x² – 4x – 6 = 0

Answer 1

(i) Draw the graph of y = 2x² – 3x – 5 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
2x2	32	18	8	2	0	2	8	18	32
– 3x	12	9	6	3	0	– 3	– 6	– 9	– 12
– 5	– 5	– 5	– 5	– 5	– 5	– 5	– 5	– 5	– 5
y	39	22	9	0	– 5	– 6	– 3	4	15

(ii) Plot the points (– 3, 22), (– 2, 9), (– 1, 0), (0, – 5), (1, – 6), (2, – 3), (3, 4), (4, 15) on the graph sheet using suitable scale.

(iii) To solve 2x² – 4x – 6 = 0 subtract 2x² – 4x – 6 = 0 from y = 2x² – 3x – 5

y = 2x² – 3x – 5
0 = 2x² – 4x – 6
       (–) (+)   (+) 
y =          x + 1

(iv) y = x + 1 represent a straight line.

x	– 4	– 2	0	2	3	4
y	– 3	– 1	1	3	4	5

The straight line intersects the curve at (– 1, 0) and (3, 4).

From the two-point draw perpendicular lines to the X-axis it will intersect at – 1 and 3.

The solution set is (– 1, 3)