Question

Draw the graph of y = x² – 5x – 6 and hence solve x² – 5x – 14 = 0

Answer 1

Let y = x² – 5x – 6

(i) Draw the graph of y = x² – 5x – 6 by preparing the table of values as below.

x	– 4	– 3	– 2	– 1	0	1	2	3	4	5	6	7	8
x2	16	9	4	1	0	1	4	9	16	25	36	49	64
– 5x	20	15	10	5	0	– 5	– 10	– 15	– 20	– 25	– 30	– 35	– 40
– 6	– 6	– 6	– 6	– 6	– 6	– 6	– 6	– 6	– 6	– 6	– 6	– 6	– 6
y	30	18	8	0	– 6	– 10	– 12	– 12	– 10	– 6	0	8	18

(ii) Plot the points (– 3, 18), (– 2, 8), (– 1, 0), (0, – 6), (1, – 10), (2, – 12), (3, – 12), (4, – 10), (5, – 6), (6, 0) and (7, 8).

(iii) Join the points by a free hand to get smooth curve.

(iv) To solve x² – 5x – 14 = 0, subtract x² – 5x – 14 = 0 from y = x² – 5x – 6.

y = x² – 5x – 6
0 = x² – 5x – 14
      (–)   (+)   (+)
y               =  8

The equation y = 8 represent a straight line draw a straight line through y = 8 intersect the curve at two places.

From the two points draw a perpendicular line to the X-axis it will intersect at – 2 and 7.

The solution is – 2 and 7