Question

Draw the graph of y = x² – 4 and hence solve x² – x – 12 = 0

Answer 1

(i) Draw the graph of y = x² – 4 by preparing the table of values as below.

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

(ii) Plot the points for the ordered pairs (– 4, 12) (– 3, 5) (– 2, 0) (– 1, – 3) (0, – 4) (1, – 3), (2, 0), (3, 5) and (4, 12). Draw the curve with a suitable scale.

(iii) To solve x² – x – 12 = 0 subtract x² – x – 12 from y = x² – 4

y = x² – 0 – 4
0 = x² – x – 12
     (–)  (+)  (–) 
y = x + 8

The equation y = x + 8 represents a straight line. Prepare a table for y = x + 8

x	– 3	– 1	0	2	4
y	5	7	8	10	12

(iv) Mark the point of intersection of the curve and the straight line is (– 3, 5) and (4, 12)

∴ The solution set is (– 3, 4) for x² – x – 12 = 0.